If the council is sole managing trustee of the charity, then it is the council as a whole that is the trustee, not individual councillors, so a meeting of the charity is a meeting of the council acting as trustee for the charity. In these circumstances it is usual for the council chair to be chairing the meetings.
People get very confused about the role of the trustee of a charity. It is often the case that the council is a custodian trustee rather than sole managing trustee and in such circumstances, the council has no role in the running of the charity. It's only function is to hold the deeds on behalf of the charity.