It's difficult to say how much the NHS pays per appointment on average, as GPs are paid per patient, I believe, whether they see their GP or not. But they are paid by the NHS, some are salaried now, but most are not.
Comparing private services offered by Virgin is not the same as them contracting to the NHS - like GPs do.
I don't have a problem with this at all - GPs have always worked this way. Doesn't matter to me if a GP works in a surgery that looks like a house or in a building that has 'Virgin Care' stamped onto every wall or is Skyping me from their living room. They're still my GP and the service is paid for by the NHS in the same way.