depending on how much you paid for the car or how much its worth consider going TPFT instead of FC, this should lower the price a bit.
As has been said, put another driver on as a named driver, preferably female. My g/f is the same age as me and has been driving 2 months more. My insurance dropped £200 when i put her on as a named driver.
Check things like: courtesy car, personal injury cover etc and decide if you need them. It can cut the price.
Paying monthly will put your price up.
Go and buy Max Power, turn to the back insurance section and start phoning the lesser well known companies. When i was 19 i wanted a Corrado G60, first insurance quote was £4400 TP only. After an hour of phoning around and playing them off i got it down to £1800 TPFT. Still too expensive but a bloody good saving.
Look at 10 month accelerated bonus schemes. I only got my own insurance about 2 years ago. Im on my 3rd 10 month scheme now. Ill have 3 years NCB (that is accepted by other companies) after just 30 months instead of 36 months. Plus the payment is cheaper, but you have to pay it more often.