I don't see a problem with American firms competing to sell their drugs to the NHS as do other companies elsewhere, or for them to offer private medicine schemes, if people wish to take them up.
A trade deal does not mean selling off the whole of the NHS to the USA. That's ridiculous. For a start it would be a very unprofitable business, as everyone keeps saying that the NHS needs more money throwing at it every year, so what company would want to take that on!
But what about the poor people, everyone will cry! However, with over 70 million people ( probably a lot more than that which is not admitted) living here and the UK population increasing by hundreds of thousands every year as well as unlimited people from abroad using our NHs for free, I don't know whom you think will pay for the NHS to continue for free at the point of delivery for ever.