No. There are strict rules on investment by local councils, which must follow government guidelines. The council must devise an investment strategy and review it at least annually. The priorities for choosing investment are, in order, security, liquidity and yield.
A substantial portion of invested funds must be as near as possible risk free, involving things like UK gilt edged securities or local government deposits. Other investments must conform to the criteria. An investment in a private company is highly unlikely to be either secure or liquid and its yield will be uncertain.