My family GP as a kid was an Indian chap called Dr Rashid, nicest guy I've ever met in the medical world. House calls were common back then after a day's work in the surgery, I remember him coming out to see me a few times when I was sick. We're only talking the late '80s here, so not exactly pre-war.
I think Rabbitstew makes a good point, and he's not portrayed it in a racist way either. I don't feel particularly comfortable when the person treating me is speaking in such a strong accent that I struggle to understand it, regardless of colour of skin. That goes as much for doctors from Glasgow as it does for doctors from Ghana: Indeed, I struggle understanding the former much more, so heaven help me if I'm ever sick north of the border!
Personally I couldn't give a fig where the person who is treating me is from, and they can all be from anywhere else for all I care. As long as the treatment is good and I can understand the treatment when explained to me, then I'm fine with that. That applies as much to anyone born in the UK as born anywhere else, which I think is reasonable enough.