I'm 19 and have a 1.2 GP active in chemical grey.
Absolute cheapest quote I can find right now (no no claims, held my license for a year) is £1200ish from swinton. At the moment I'm with direct line, paying £1,700ish but my policy expires in march so I'm waiting the remaining time out then changing as my old policy expires so I get my no claims.
Theres not much you can do tbh aged 20. It's going to be expensive either way.
All you can do is 'live in a better area' this will save you up to £300 (done identical quotes using different postcodes), get older. Try adding a parent to the policy (for me this either makes no difference or makes it more expensive).
Your basically just going to have to build your no claims.