Yes he is correct. Local Government Act 1972 section 84
"A person elected to any office under this Act [F11or elected as an elected mayor]may at any time resign his office by written notice delivered—
(a)except in a case falling within paragraph (b), (c) or (d) below, to the proper officer of the council;
(b)in the case of a person elected to a corporate office in a London borough, to the proper officer of the borough;
(c)in the case of a parish or community councillor, to the chairman of the parish or community council;
(d)in the case of a chairman of a parish or community council or of a parish meeting, to the council or the meeting, as the case may be;
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.