POWER OF ATTORNEY

      Know all by these presents, that the undersigned hereby constitutes and
appoints each of Brian G. Drazba and David M. Urso, or either of them signing
individually, and with full power of substitution, the undersigned's true and
lawful attorney-in-fact to:

(1) prepare, execute in the undersigned's name and on the undersigned's behalf,
and submit to the U.S. Securities and Exchange Commission (the "SEC") a Form ID,
including amendments thereto, and any other documents necessary or appropriate
to obtain codes and passwords enabling the undersigned to make electronic
filings with the SEC of reports required by Section 16(a) of the Securities
Exchange Act of 1934, as amended (the "Exchange Act") or any rule or regulation
of the SEC;

(2) execute for and on behalf of the undersigned, in the undersigned's capacity
as an officer and/or director of MEI Pharma, Inc. (the "Company"), Forms 3, 4,
and 5 in accordance with Section 16(a) of the Exchange Act and the rules
thereunder;

(3) do and perform any and all acts for and on behalf of the undersigned which
may be necessary or desirable to complete and execute any such Form 3, 4, or 5,
complete and execute any amendment or amendments thereto, and timely file such
form with the SEC and if required, any stock exchange or similar authority; and

(4) take any other action of any type whatsoever in connection with the
foregoing which, in the opinion of such attorney-in-fact, may be of benefit to,
in the best interest of, or legally required by, the undersigned, it being
understood that the documents executed by such attorney-in-fact on behalf of the
undersigned pursuant to this Power of Attorney shall be in such form and shall
contain such terms and conditions as such attorney-in-fact may approve in such
attorney-in-fact's discretion.

      The undersigned hereby grants to such attorney-in-fact full power and
authority to do and perform any and every act and thing whatsoever requisite,
necessary, or proper to be done in the exercise of any of the rights and powers
herein granted, as fully to all intents and purposes as the undersigned might or
could do if personally present, with full power of substitution or revocation,
hereby ratifying and confirming all that such attorney-in-fact, or such
attorney-in-fact's substitute or substitutes, shall lawfully do or cause to be
done by virtue of this power of attorney and the rights and powers herein
granted. The undersigned acknowledges that the foregoing attorneys-in-fact, in
serving in such capacity at the request of the undersigned, are not assuming,
nor is the Company assuming, any of the undersigned's responsibilities to comply
with Section 16 of the Exchange Act and the rules thereunder.

      This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file Forms 3, 4, and 5 with respect to the
undersigned's holdings of and transactions in securities issued by the Company,
unless earlier revoked by the undersigned in a signed writing delivered to the
foregoing attorneys-in-fact.

      IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to
be executed as of this 22nd day of February, 2018.

/s/ Frederick W. Driscoll
Frederick W. Driscoll