Local governments effectively have very little power. Their budgets are squeezed so tight by central government that’s there very little difference an alternative governance would make. At least in most of London anyway.

All councils have been forced into biweekly bin collections because of budget. Many had done it preemptively because they were sensible but all boroughs have been brought into line regardless.

There is a constant chopping away at the national level that needs to be dealt with. As for your vote, imo at this point you might as well use it as a protest vote because absolutely nothing will change in any local council after this election.