I have no problem with phone consultations, but our family nearly suffered the loss of a member when the system failed her.
What would worry me is that if a practice, or private company started employing, overseas Gps, who were domiciled in their native country and were not familiar with the UK or our medical system problems could arise.
Medecine is 50% science and 50% human relations and there ar so many nuances, minor cultural attitudes, language subtleties, that would be lost where the GP is not familiar with the country, misunderstandings when notes are passed on to the GP seeing the patient - and how would the doctor be supervised to check that they were working in a professional manner and not taking patient calls, while stirring lunch, or lounging in the garden.
As I said, I have no problem with telephone appointments, but not with doctors conducting them from another country. That would apply even if the doctor was British.