I had no trouble registering with a GP and then getting in almost at once to see him (the surgery has same-day appointments). You will, however, have to show your visa (spouse or fiancÚ works) to register, but won't need anything else.
Here's the NHS site explaining how to register:
How do I register with a GP?
Oral contraceptives are free. My GP gives me a prescription for six months at a time.