I queried the status of our town clerk based on your advice and this is the reply I got:
The Council does not require a byelaw for such matters. In fact, it would be unlawful, as a byelaw has been judicially defined as “an ordinance affecting the public or some portion of the public, imposed by some authority clothed with statutory powers, ordering something to be done or not to be done and accompanied by some sanction or penalty for its non-observance” (Kruse v Johnson [1898] 2 QB 91).
While town and parish councils lack statutory authority to appoint a leader, this does not prohibit them from doing so. An increasing number of politically divided town and parish councils are appointing leaders. However, this is not a statutory role like the chair of the council, and the leader has no delegated authority as per section 101 of the Local Government Act 1972. The leader plays a crucial role in raising business and lobbying other councillors on issues, in line with SLCC and NALC advice notes.