Jim, contrary to the previous posts, your obligation to your current insurance company is to pay the complete annual premium, not to reimburse them for any claims that they have had to pay! So, if you paid your premium up front, then you can move to another insurer (you won't get any of your premium back though.) If you are paying monthly, you will have to pay the outstanding premium for the full year, as most insurance is an annual contract, and they have fulfilled their side of the contract by dealing with your claim.
The only other thing to watch out for is transferring protected no claims bonus when there has been a claim - some companies will accept it 'as is' and some won't! Make sure you are well aware of all the facts before acting.