This isn't re benefits but re: named GP If your GP practice has more than one GP, you should be able to choose which doctor you see regularly, even if they are not the 'named' one the NHS has you registered with. Have you met any of the others you know you can talk to +/- has been there a while so likely to say rather than move on in a couple of years? I agree with you that 'cured' emphysema is 'interesting', but now he/she has gone thoroughly through you notes so knows your history, if you felt at meeting you could talk to them maybe give them a try?
I've never been registered with the GP I see - I've registered with a practice & admin-wise they've registered me with whichever doctor had space on their list. Then when I went for my new patient assessment the practice nurse has suggested the GP she thought would suit me. When he retired, I went back to same nurse to ask if she thought I'd get on with new one. I only get reminded who my official GP is when a get eg cervical screening letters automatically generated by wider NHS!