We had the same problem when we rented a house in Haredon Close near you. It took 5 months to finally find a GP, in the end I called the NHS and they forced the Brockley Surgery to take us. At the time, it was a bit of a walk for us but the house we have now bought is close to the surgery, as we are now near Brockley rise so it is a short walk.

I have also heard good things about the Jenner surgery. Do not dispear, call the NHS, explain the problem and they will assign you to a local GP and will send you a letter with the GP they have assigned to you, that you then take to the GP and they cannot turn you away with that ketter. it worked for us.