Hannah Fearn has an update on Council Tax trends here. Most of the Councils with rises are sticking to below the rate at which you trigger a referendum, for reasons I explained here. Her reference "If councils all agreed to accept the government bung, further down the line those very authorities would only face criticism from the communities minister for allowing essential services to close" probably needs a bit more explanation.
The government has been using a small grant to Councils that freeze Council Tax to effectively bribe authorities into doing that. However, the grant is time limited, and the government can simply revoke it at will. Indeed in recent years, the grant does not even fully compensate for the loss of a 2% Council Tax rise. Councils that accept the grant are therefore effectively eroding their base budget, which at some point will have to lead to further cuts in services.
Incidentally, the recent Brent budget consultation concluded that the public didn't realise that Council Tax has been frozen for some years in Brent. Apparently, most people thought it had gone up.