Hi Guiditta
I'm afraid your question is outside the scope of this forum - we don't deal with council issues. I do know that while many people were exempt from paying council tax, many councils have removed those exemptions (which is their right) and are asking people to make some sort of contribution. (And I do know someone who has migrated from ESA to UC and lives in Lambeth and is having to pay something for the first time). I'm afraid it is something you will have to raise with them.
BIS
Nothing on this board constitutes legal advice - always consult a professional about specific problems