Go on comparison websites. Cheap companies for adults doesn't necessarily mean cheap for young drivers. With my daughter's low mileage, where it's kept, value of the car and picking 3rd party only knocked some off.
I seen several reports, here on AB and elsewhere, of young drivers getting a lower quote by adding one of their parents onto the policy as a 'named driver'. It might be worth looking into.
i-Kube offers cheaper insurance to young drivers who don't use their car between 11pm and 5am.
Coverbox calculates premiums based upon anticipated mileage and even gives a refund if the actual mileage is lower:
http://www.coverbox.co.uk/