No. The legislation is contained in the Local Government and Housing Act 1989, section 13.
"...a person who -
(a) is a member of a committee appointed under a power to which this section applies by a relevant authority and is not a member of that authority;
shall for all purposes be treated as a non-voting member of that committee, joint committee or, as the case may be, sub-committee."
The Secretary of State has the power to grant exemptions for specific purposes and there are currently four contained in the Parish and Community Councils (Committees) Regulations 1990:
(a) the management of land owned or occupied by the council;
(b) where the council are a harbour authority as defined in section 57(1) of the Harbours Act 1964(1), their functions as such;
(c) any function under section 144 of the 1972 Act(2) relating to the promotion of tourism;
(d) any function under section 145 of the 1972 Act relating to the management of a festival.