What will your visa status be? If you are just coming to visit, or for less than six months, then it you won't be entitled to NHS treatment and will have to get insurance.
Otherwise, birth control will be free. It may be an idea to go to a Family Planning Clinic in the first instance than a GP. In my experience, they are more likely to discuss all your birth control options and as well as knowing what is comparable with the pill you are using now they will also be in a position to discuss whether we have something over here which is even better.
An FPC is likely to give you three months of the pill initially, and then when you come back, if everything is oaky, they will give you six months.
Vicky