Not any sort of recommendation, just my experience.
After many years of switching around every couple of renewals, I ended up with my 1.0L Yaris with Aviva on a pretty much full spec policy, business/protected NC etc with several nice features like no charge for any changes and free short term FC cover on anyone else's car if you give the details in advance. No extra for paying monthly DD. It was slightly higher than other "premium" brand insurers but not a lot, especially allowing for the "extras".
They promised to give a renewal quote no higher than a new customer. The annual renewal went down.
When I got the Jazz I swapped the cars on that policy, upped the annual mileage, it added 60p/month, no charge to change.
Quotemehappy are Aviva's internet only brand, and they are similar - none of the administration charges you get with other insurers, including for substitutions. You probably don't get all the frills, but you can add what you need, and other half still can't get a cheaper quote anywhere else. Likewise, the price on comparison sites always appears to be the same as the renewal. We have no complaints.
I do agree about some of the budget insurers though, some of them have poor reputations - the biggest problems start when you need them to help you fight a claim against you. The one I try to avoid in particular is BISL (Budget Insurance Services Limited), and any of their many white label insurance brands. I know a few people who have had major issues with fault and no-fault claims.