Presently, it is legal to vote in the local elections of two separate local councils if you live in, and are registered in, two different constituencies.
You may be interested in these active petitions
This practice can lead to fraud, with voters able to register at addresses in places they have no physical connection with, to aid their chosen party.
End this practice immediately. It benefits only the few, and potentially jeopardises the voting power of many.
https://www.gov.uk/elections-in-the-uk/local-government