Exhibit 5.1

Dear Sirs

Prospectus Supplement

1.                                      Background

We have acted for Adaptimmune Therapeutics plc, a public limited company incorporated under the laws of England and Wales (the “Company”), as its legal advisers in England in connection with the offering (the “Offering”) by the Company of 85,800,000 new ordinary shares of £0.001 each in the Company (the “New Shares”).  The New Shares are to be offered in the form of 14,300,000 American Depositary Shares (“ADSs”).  Each ADS represents 6 ordinary shares of the Company.  The underwriters to the Offering have the right to purchase up to an additional 2,145,000 ADSs, representing 12,870,000 new ordinary shares of £0.001 each in the capital of the Company (the “Further Shares”).

This opinion is being furnished in connection with the Registration Statement on Form S-3 (No. 333-212713) (the “Registration Statement”) filed with the Securities and Exchange Commission (the “SEC”) under the Securities Act of 1933, as amended (the “Securities Act”) and the rules and regulations promulgated thereunder (the “Rules”), the prospectus included within the Registration Statement, and the prospectus supplement dated 22 March 2017 to be filed with the SEC pursuant to Rule 424(b) of the Rules (the “Prospectus Supplement”).

We understand that the ordinary shares of £0.001 each in the capital of the Company are not, and are not intended to be, admitted to trading on any market or exchange, or otherwise listed, in the United Kingdom.

This is a legal communication, not a financial communication. Neither this nor any other communication from this firm is intended to be, or should be construed as, an invitation or inducement (direct or indirect) to any person to engage in investment activity.

Mayer Brown International LLP is a limited liability partnership (registered in England and Wales number OC303359) which is authorised and regulated by the Solicitors Regulation Authority. We operate in combination with other Mayer Brown entities with offices in the United States, Europe and Asia and are associated with Tauil & Chequer Advogados, a Brazilian law partnership.

We use the term “partner” to refer to a member of Mayer Brown International LLP, or an employee or consultant who is a lawyer with equivalent standing and qualifications and to a partner of or lawyer with equivalent status in another Mayer Brown entity. A list of the names of members of Mayer Brown International LLP and their respective professional qualifications may be inspected at our registered office, 201 Bishopsgate, London EC2M 3AF, England or on www.mayerbrown.com.

2.                                      Examination and enquiries

2.1                               For the purpose of giving this opinion, we have examined:

(a)                                 a copy of the Prospectus Supplement; and

(b)                                 a certificate dated 22 March 2017 (the “Reference Date”) signed by the company secretary (the “Officer’s Certificate”) relating to certain factual matters as at the Reference Date and having annexed thereto copies (certified by the company secretary as being true, complete, accurate and up-to-date in each case) of the following documents:

(i)                                     the Company’s certificate of incorporation, certificates of incorporation on change of name, memorandum of association and articles of association;

(ii)                                  shareholder resolutions passed at the annual general meeting of the Company on 17 December 2015 authorising the directors of the Company for the purposes of s551 Companies Act 2006 and conferring power on the directors of the Company pursuant to s570 Companies Act 2006 (the “Shareholder Resolutions”);

(iii)                               minutes of meetings of the board of directors of the Company held on 21 July 2016, 6 October 2016 and 12 January 2017 at which it was resolved, inter alia, to proceed with the Offering and to constitute a financing committee of the board of directors of the Company (the “Committee”) and subsequently to revise the terms of reference of the Committee; and

(iv)                              minutes of meetings of the board of directors of the Company held on 21 March 2017 and 22 March 2017 at which it was resolved, inter alia, to approve and file the Prospectus Supplement and to allot the New Shares;

(c)                                  draft minutes of a meeting of either the Committee or the board of directors of the Company to be held to resolve, inter alia, to allot Further Shares in the event that the underwriters to the Offering exercise their right to purchase the same (such draft resolutions, together with the resolutions of the board of directors of the Company of 21 July 2016, 6 October 2016, 12 January 2017, 21 March and 22 March 2017, the “Board Resolutions”, and the Board Resolutions together with the Shareholder Resolutions, the “Corporate Approvals”); and

(d)                                 a copy of the executed underwriting agreement dated 22 March 2017 in connection with the Offering between (1) the Company and (2) Citigroup Financial Markets, Inc., Cowen and Company, LLC and Leerink Partners LLC as representatives of the several underwriters named therein (the “Underwriting Agreement”), but excluding any exhibits thereto.

2.2                               For the purpose of giving this opinion, we have:

(a)                                 on 17 March 2017 made, and on 22 March 2017 updated, an online search of the register kept by the Registrar of Companies in respect of the Company (the “Company Search”); and

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(b)                                 made a telephone enquiry in respect of the Company of the Central Index of Winding Up Petitions on 22 March 2017 at 10:40 a.m. (GMT) (the “Telephone Search”, and together with the Company Search, the “Searches”).

2.3                               For the purposes of giving this opinion, we have only examined and relied on those documents and made those searches and enquiries set out in paragraphs 2.1 and 2.2 respectively.  We have made no further enquiries concerning the Company or any other matter in connection with the giving of this opinion.

2.4                               We have made no enquiry, and express no opinion, as to any matter of fact.  As to matters of fact which are material to this opinion, we have relied entirely and without further enquiry on statements made in the documents listed in paragraph 2.1.

3.                                      Assumptions

3.1                               In giving this opinion we have assumed:

(a)                                 the genuineness of all signatures, seals and stamps;

(b)                                 that each of the individuals who signs as, or otherwise claims to be, an officer of the Company is the individual whom he or she claims to be and holds the office he or she claims to hold;

(c)                                  the authenticity and completeness of all documents submitted to us as originals;

(d)                                 the conformity with the original documents of all documents reviewed by us as drafts, specimens, pro formas or copies and the authenticity and completeness of all such original documents;

(e)                                  that each of the meetings referred to in paragraphs 2.1(b)(ii), 2.1(b)(iii), 2.1(b)(iv) and 2.1(c) (Examination and enquiries) was or will be duly convened, constituted and held in accordance with all applicable laws and regulations; that in particular, but without limitation, a duly qualified quorum of directors or, as the case may be, shareholders was or will be present in each case throughout the meeting and voted or will vote in favour of the resolutions; and that, in the case of a board meeting, each provision contained in the Companies Act 2006 or the articles of association of the Company relating to the declaration of directors’ interests or the power of interested directors to vote and to count in the quorum was or will be duly observed;

(f)                                   that in each case the documents referred to in paragraphs 2.1(b)(ii), 2.1(b)(iii), 2.1(b)(iv) and 2.1(c) (Examination and enquiries) are or will be a true record of the proceedings of the relevant meeting and that each resolution recorded in those documents has not been and will not be amended or rescinded and remains or will remain in full force and effect;

(g)                                  that the directors of the Company acted and will act in accordance with ss171 to 174 Companies Act 2006 in approving the resolutions recorded in the minutes referred to in paragraphs 2.1(b)(iii), 2.1(b)(iv) and 2.1(c) (Examination and enquiries); and that all actions to be carried out by the Company pursuant to the Corporate Approvals are or will be in its commercial interests;

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(h)                                 that no agreement, document or obligation to or by which the Company (or its assets) is a party or bound and no injunction or other court order against or affecting the Company would be breached or infringed by the matters contemplated by the performance of the actions to be carried out pursuant to, or any other aspect of the transactions contemplated by, the Corporate Approvals;

(i)                                     that the information disclosed by the Searches is true, accurate, complete and up-to-date and that there is no information which, for any reason, should have been disclosed by those Searches but was not so disclosed;

(j)                                    that the Company is and will at all relevant times remain in compliance with all applicable anti-corruption, anti-money laundering, anti-terrorism, sanctions, exchange controls and human rights laws and regulations of any applicable jurisdiction;

(k)                                 that all consents, licences, approvals, authorisations, notices, filings and registrations that are necessary under any applicable laws or regulations in order to permit the performance of the actions to be carried out pursuant to the Corporate Approvals have been or will be duly made or obtained and are, or will be, in full force and effect;

(l)                                     that there are no provisions of the laws of any jurisdiction outside England and Wales that would have any implication for the opinions we express and that, insofar as the laws of any jurisdiction outside England and Wales may be relevant to this opinion letter, such laws have been and will be complied with;

(m)                             that each party to each agreement or instrument pursuant to which New Shares or Further Shares are offered, issued and/or sold will have the capacity to enter into and deliver, and to exercise its rights and perform its obligations thereunder, will have taken all necessary corporate action to authorise that entry, delivery, exercise and performance, and will not be prohibited by any applicable law from that entry, delivery, exercise and performance; that each such agreement or instrument will have been duly executed by or on behalf of each party to it; and that the obligations created by each such agreement or instrument will constitute the legal, valid, binding and enforceable obligations of each of the parties to it under the laws by which it is expressed to be governed;

(n)                                 that no New Shares or Further Shares are acquired as a consequence of a communication made in breach of s21(1) Financial Services and Markets Act 2000;

(o)                                 that the New Shares and Further Shares will be offered and sold in accordance with all applicable laws;

(p)                                 that no application has been or will be made for any New Shares or Further Shares to be listed or admitted to trading on a regulated market situated or operating in the United Kingdom;

(q)                                 that on each date on which any New Shares or Further Shares are allotted and issued (each an “Allotment Date”) the Company will have complied with its articles of association and all applicable laws relevant to the allotment and issue of those New Shares or Further Shares;

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(r)                                    that as at each Allotment Date the documents examined, and the results of the searches and enquiries made, as set out in paragraph 2 (Examination and enquiries) would not be rendered untrue, inaccurate, incomplete or out-of-date by reference to subsequent facts, matters, circumstances or events;

(s)                                   that the aggregate issue price in respect of each New Share and Further Share is not less than the nominal value of that New Share or Further Share;

(t)                                    that all New Shares and Further Shares will be allotted and issued pursuant to the authority and power granted to the directors of the Company respectively under the Shareholder Resolutions and that that authority and that power are and shall remain unutilized to a sufficient extent to enable the issue and allotment of the New Shares and Further Shares;

(u)                                 that the directors of the Company as at each Allotment Date will have validly resolved to allot and issue the relevant New Shares or Ordinary Shares in accordance with the Underwriting Agreement and the Prospectus Supplement; and

(v)                                 that there will be no fact or matter (such as bad faith, coercion, duress, undue influence or a mistake or misrepresentation before or at the time any agreement or instrument is entered into, a subsequent breach, release, waiver or variation of any right or provision, an entitlement to rectification or circumstances giving rise to an estoppel) which might affect the allotment and issue of any New Shares or Further Shares and no additional document between any relevant parties which would or might affect this opinion and which was not revealed to us by the documents examined or the searches and enquiries made by us in connection with the giving of this opinion.

3.2                               In relation to paragraph 3.1(i), it should be noted that this information may not be true, accurate, complete or up-to-date.  In particular, but without limitation:

(a)                                 there may be matters which should have been registered but which have not been registered or there may be a delay between the registration of those matters and the relevant entries appearing on the register of the relevant party;

(b)                                 there is no requirement to register with the Registrar of Companies notice of a petition for the winding-up of, or application for an administration order in respect of, a company.  Such a notice or notice of a winding-up or administration order having been made, a resolution having been passed for the winding-up of a company or a receiver, manager, administrative receiver, administrator or liquidator having been appointed may not be filed with the Registrar of Companies immediately and there may be a delay in any notice appearing on the register of the relevant party;

(c)                                  the results of the Telephone Search relate only to petitions for the compulsory winding up of, or applications for an administration order in respect of, the Company presented prior to the enquiry and entered on the records of the Central Index of Winding Up Petitions.  The presentation of such a petition, or the making of such an application, may not have been notified to the Central Index or entered on its records immediately or, if presented to a County Court or Chancery District Registry, at all; and

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(d)                                 in each case, further information might have become available on the relevant register after the Searches were made.

4.                                      Opinion

4.1                               On the basis of the examination and enquiries referred to in paragraph 2 (Examination and enquiries) and the assumptions made in paragraph 3 (Assumptions), we are of the opinion that the New Shares and the Further Shares will, when the names of the holders of such New Shares and Further Shares respectively are entered into the register of members of the Company and subject to the receipt by the Company of the aggregate issue price in respect of all the New Shares and the Further Shares respectively in accordance with the Underwriting Agreement and the Prospectus Supplement, be validly issued, fully paid and no further amount may be called thereon.

4.2                               This opinion is strictly limited to the matters expressly stated in this paragraph 4 and is not to be construed as extending by implication to any other matter.

5.                                      Law

5.1                               This opinion and any non-contractual obligations arising out of or in connection with this opinion shall be governed by, and construed in accordance with, English law.

5.2                               This opinion relates only to English law (being for these purposes, except to the extent we make specific reference to an English law “conflict of law” (private international law) rule or principle, English domestic law on the assumption that English domestic law applies to all relevant issues) as applied by the English courts as at today’s date, including the laws of the European Union to the extent having the force of law in England.

5.3                               We do not undertake or accept any obligation to update this opinion to reflect subsequent changes in English law or factual matters.

5.4                               We express no opinion as to, and we have not investigated for the purposes of this opinion, the laws of any jurisdiction other than England.  It is assumed that no foreign law which may apply to the matters contemplated by the Prospectus Supplement, the Offering, the Company, any document or any other matter contemplated by any document would or might affect this opinion.

We hereby consent to the filing of this opinion as an exhibit to the Prospectus Supplement.  In giving such consent, we do not admit that we are in the category of persons whose consent is required under section 7 of the Securities Act or the Rules.

Yours faithfully

/s/ Mayer Brown International LLP

Mayer Brown International LLP

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