I did a couple of phone call renewals with the AA after getting high quotes, they dropped the renewal down to competitive amounts (from comparison sites), so I was fine with that. The following year I just got fed up with the game and went with LV, who get pretty good reviews on trustpilot etc. I haven't had to make any claims etc so can't really comment from first hand experience.
I do have an Aviva policy which has some advantages (no charge for changes, fully comp cover for a limited period on someone else's car etc) albeit at a modest extra cost compared to others. They promise to give renewal quotes no higher than a new customer would get, and last renewal actually went down.
I haven't had to claim, but review ratings aren't particularly good so I keep my fingers crossed I won't.
It's a lottery. As Jocko says, I've heard that about 3 weeks before renewal is the best time to get the most competitive quotes (shows you are prepared to take action in good time etc, marketing psychology).