A person elected to any office under this Act or elected as an elected mayormay at any time resign his office by written notice delivered—
and his resignation shall take effect upon the receipt of the notice by the person or body to whom it is required to be delivered.
A person elected or appointed to an office under Part . . . IV of the Local Government Act 1985 may at any time resign his office by written notice delivered to the proper officer of the authority of which he is a member and his resignation shall take effect upon the receipt of the notice by that officer.