Hi Wendy,
as I live In Germany I cannot give you direct advice for UK or the NHS.
But I also had difficulties finding a doctor who would help me.
The following two things helped me, finding a doctor and contacts:
Write also "UK" in the subject of your topic. Many of the people here are from US or elsewhere. Anyone from the UK could find you better. This is now important, and if you find help anyone who is looking for that much later could find you. Thus I found two other patients from Germany.
Secondly, contact Prof. Amoura and Prof. Pecker from the "Disorder Details" section, and ask them for advice and if they know someone in the UK. Mark Pecker is very helpful and friendly. He knows a doctor in Germany, made contacts, and from him respectively at his hospital I get my IVIGs.
I wish you the very best.
Andreas