Daisy couldnt register with GP on fiance visa; no problem once she had FLR. When we arrived at Heathrow I guess it took about 45 minutes to get through immigration: so it will depend on time of day, number of staff, etc.
I came here on a fiance visa in 2006 my fiancee now husband was able to register me with his gp when i was still holding a fiancee visa. I Dont know if that has changed.