Hi there,
Most local health centres run family planning clinics. Just look in the phone book for the nearest health centres phone number, give them a ring and ask them when they hold their clinics. They can give you all sorts of advice and give you most types of contraception for free. I was too embarrassed to go to my GP so always went to family planning clinics. There are also now alot of sexual health drop in clinics. Again the phone book will point you in the direction of those.
Good luck!