Car Insurance - shop around... Can you do this if a claim is still open?

Sniblet

Martin is saying to check if you can get a cheaper deal elsewhere before the end of this year, so with this in mind, I've just spoken with my current insurers and after a non fault claim (a pickup backed into my parked car while I was shopping - gah! ) , I've been told that the claim is still open. This is due to third party arguing with car hire charges.
Is it possible to shop around still with a claim still open? I'm assuming not but wanted to check wit all you savvy MSE'ers whether I can or cannot shop around now? 
Thanks in advance for your response!
S  

[Deleted User]

You can shop around. You will have to list the claim as at fault until they pay up fully. The quotes you get will reflect that, and once it's closed as non-fault you will be able to ask for a partial refund.

I'd suggest waiting until the claim is closed. Then shop around and you can see exactly how much it's added on to your premium, and claim it back from the third party.

Sandtree

You can get prices but NCD can only be used on one policy at a time  and you cannot cancel the existing policy whilst there is an open claim on it (it can lapse at the natural end though) and so if you were to buy the new policy before the old one is cancelled would have to be on 0 NCD basis and most likely the claim would have to be declared as "fault" as claims almost universally are defaulted to fault whilst open.

You could ask the new insurer before buying about moving the NCD across later and/or changing the claim to non-fault but both are unlikely to be acceptable plus you'd be paying two premiums for a time and the new one likely to be higher