To be honest, your best bet is a price comparison site.
I can tell you that I am with Admiral and they were untouchable with my latest car which is a 1.6 turbo sporty little number and they were also untouchable when I had my 2.0 litre Renault Clio pocket rocket and also my 2.0 Honda Civic.
But in between I had a bog standard Vauxhall Astra hatchback and their prices were astronomical. It didnt make any sense.
So I would say, to use one of the main comparison websites and fill out all the details as accurately as you can.
Then pay
close attention to what is included in each price returned as they vary from £0 voluntary excess to £400, and thats on top of the compulsory excess.
Then others will give free legal cover, breakdown, courtesy car, etc etc whilst others will charge extra for these 'perks'.
So the 'cheapest' isnt always the cheapest.
But if you fill it in properly and play close attention to the results before choosing then you shouldnt go far wrong.
Having said that, I was talking to a lad who had just passed his test and was driving a 1.2 engine car and the 'cheapest' he was able to get was in excess of £2,000 so you may want to be sitting down when you get the quote....
My cousin who is in his teens has just started driving and has cheaper insurance as he has a policy which has an 11pm curfew on it. The car is fitted with a tracking device and if he is out after 11 then he is hit with a fine. If he is home by 1 every night then there is no problem and his insurance is cheaper as a result. Personally, I would have hated this idea when I was that age, but the option is there.....