Nothing in this subchapter and §§ 43-119 and 43-125 shall be construed so as to affect the authority vested in the Mayor by Reorganization Plan No. 5 of 1952. The performance of any function vested by this subchapter and §§ 43-119 and 43-125 in the Mayor or in any office or agency under the jurisdiction and control of said Mayor may be delegated by said Mayor in accordance with § 3 of such Plan.