There are many tips for reducing your premium as people have said, obviously the area where you live and your age / experience are the major deciders on cost but all the little things help so it is worth playing about online to see what is cheapest.
eg. a garaged car is less risk than a street parked car, a mileage of 8,000 is a lot less than a mileage of 15,000, until last year I had my Dad and Mum on my policy to bring the price down, stating the car has an immobiliser if it has one also helps.
In recent years the difference in price between fully comp and TPFT seems to have narrowed. It used to be loads cheaper to go 3rd party but not so much any more. You will find that once you have paid your young drivers excess that you won't be left with much of a payout anyway!