If you tell them they WILL charge you for the entire time, ignorance is no defence, and they won't do any of that 50/50 stuff. You either have to cop for the lot, say you've just moved in and want to set up a direct debit, or just keep quiet and never pay till you move out.

In out last house the previous owner kept paying our rates by direct debit (silly cow). Seeing as she messed us around with the house sale we let her pay for two years. Luckily our neighbour worked for the local water company, and a couple of months before we moved out she quietly changed the records so it was in our name.