Young driver here.
I went with Hastings for my first year of driving, they were the cheapest on a 1.9TDI Passat Estate though it took ALOT of ringing around, doing online quotes and talking to brokers to get the price I got for that car. Now in my second year of driving on a 1.6HDI Peugeot Im with PremiumChoice. Both times Ive refused to have a blackbox though quotes will be considerably lower with a blackbox, Hastings and Premium Choice were the cheapest when doing online quotes with a blackbox.
EDIT - I'm paying £950 Fully Comp, parked on a street In a rough-ish area, no no claims (I had a minor bump last year) No modifications, upto 20,000 miles per year with Commuting, Social., Domestic and pleasure. Compared to other people I know my age driving smaller engined petrol cars (boyracer cars like corsas, fiestas, puntos) my quote is VERY low.