Tesco have been great for us for the last 2 years. However this year we got a quote from First Assure and they came back £200 cheaper! I think it depends on what car you have though with them and your age.
Log in to confused.com. You put in all of your details once and they trawl through loads of insurers to find you the cheapest quote. I was with elephant last year as they were really cheap but tried to put it up by £150 this year so I went with Admiral(same company) they were the cheapest - it doesn't make any sense.
Companies i would recommend you don't touch with a barge pole:
The AA- they're actually a broker, I ended up being insured with a company called Groupama who were AWFUL when someone ran into me in a car park. The AA wouldn't even talk to me and said they couldn't contact groupama so I had to do it all myself!
Admiral- similar reason to above! Didn't even get a certificate of insurance for over 6 months!
Have now decided that it isn't worth going with the cheapest I can find... but sticking with someone that comes recommended!