Best thing to do is go to NHS direct (
http://www.nhsdirect.nhs.uk/), click on Local Services Database, and in the "Find NHS Services" box, select "Doctor" and enter your postcode.
It'll show you the GP (General Practitioner, a family doctor) surgeries that are near where you live.
Generally people don't register with GPs unless they're ill, so the receptionist is likely to book you in for an emergency consultation without registering first.
You will be expected to register afterwards, so the can claim back from the NHS.
You'll be asked fill in a form to get a medical card, and also to have a medical.