You can register with a doctor even if you don’t have a permanent address. For example, at:
Gordon House Surgery
78 Mattock Lane, Ealing, London W13 9NZ
Tel. 020 8799 5699
Monday – Friday: 8:00am – 1:00pm, 2:00pm – 6:30pm
Saturday: 9:00 am – 12:00 pm (by appointment only, no emergencies)