Ah at last a topic on my specialist subject.
I don't think any of the big suppliers will charge you a cancellation fee if you move house, but not everyone will allow you to take your product from one property to the next. You may have to take out a new contract at your new house which may be more expensive than your old one as the same product my not be available.
Edf will let you take your product with you even if your moving to a new area. They will also give you same discount for paying by direct debit whole amount as the standard fixed direct debit. Not all suppliers do this, Edf started doing this on 31st December 2013 so you should have seen a new discount appear on your bill.
Also Edf have no cancellation fees so you are free to leave any product whenever you want, there are no tie ins.
You'll also be able to win Zingy merchandise soon. People go mad for that thing!