The council doesn't need council tax
 

The council gets all it needs for the services from central government. The council charges council tax in order to free up the money they get from central government. They then use this freed-up money for things that have nothing to do with services. e.g. they invest it - if the investments go wrong, all they have to do is raise council tax and the sheeple carrying paying because they think it is needed for the services.