No, not at all. If I am referred to any consultant, I look them up on the internet to see their track record. What they look like is of no concern to me, only that they know what they are doing. Many doctors from the Asian subcontinent are talented and skilled. What they wear out of work is not my business.
Leahbee, it's not uncommon for patients to have to travel to centres of excellence these days - it's more cost effective for the NHS to centralise speciality areas, than keep open small expensive units where consultants have to dash from one to the other. Where possible, the patient has choice about where they go.
My OH had to go for a scan some years back - there was a many-week wait at our local unit, the GP arranged for him to go to Belgium for it. It was brilliant.