We had exactly the same problem. They needed a visa with at least 6 months left to run. I didnt find the Home Office or NHS sites very specific with advice.

I think the problem is that there is no rule in place and it is left to the discretion of each surgery. It may also be in part the jobsworth nature of some receptionists.

Once Daisy had her FLR there was no problem at all.

The definitive answer would come from your local Family Practicioner Committee.