As far as I know, there aren't separate OBGYNs in the UK (unless you need a specialist referral) - everything is done through your GP surgery.
If you need birth control, you either get it from your GP through a regular appointment (no check up needed for it other than blood pressure and perhaps a weight check), or you can just go to a GUM/Family planning clinic and ask for it.
As far as I am aware, GPs usually issue birth control either in 6-monthly or 12-monthly prescriptions and you should only need to see the GP for a review once a year (maybe twice - probably depends on your circumstances). Also, all birth control prescriptions are free of charge.
If you need a pap smear, it is usually done by one of the nurses at your GP surgery (standard is once every 3 years between the ages of 25 and 50, then every 5 years between 50 and 64, unless you have need for more regular check-ups (i.e. family history etc.)). You just make an appointment with a nurse every 3 years.