According to their website “the Local Government Association [LGA] Labour Group exists to provide a strong voice for Labour in local government. We represent and support Labour Groups in England and Wales and the Labour councillors within them.”

There is much useful information on their website — https://www.local.gov.uk/lga-labour

There is also an Update from the Leader of the LGA Labour Group at https://content.govdelivery.com/accounts/UKLGA/bulletins/295058b which might be of interest.