Don't go near Norwich Union/Aviva. I had a dreadful time with them, and made two written complaints, neither of which received a response. Not that I would have gone with them again, but they also refused to insure me again when it came to renewal time. I suspect that was their way of dealing with my complaint.
Hastings Direct are cheap, but awful. I was insured with them, and had to make two claims (both rear-end shunts, so not my fault). Had lots of trouble with them. They refused to give me a courtesy car unless I used their repairer, which I was unhappy with as they were not Merc specialists. They also messed the garage around with payment for the work when it was done, to the extent that the garage said they would not undertake further work with them. I wrote a letter of complaint to them as well, which was also met with no response.
Many years ago, I made a claim with Endsleigh, when my car was stolen by joyriders: seem to recall that was handled ok.
I have been with the AA several times, but don't think I had to claim. They would not give me a quote for my current car.
I'm with Direct Line at the moment. Very cheap quote, although they have been a bit funny about my no claims bonus: they seem to have a policy of not accepting renewal letters from brokers as evidence of no claims entitlement. Currently still trying to sort that one out, as the underwriter of my last policy (the dreadful Aviva) are refusing to issue a confirmatory letter, saying that is down to the broker. Direct Line say they will not accept a letter from a Broker etc.