Never happen - she'd be less likely to privatize the NHS than most PMs. She always regarded it as a "third rail"; in David Owen's autobiography he commented that he trusted the Tories under Thatcher with keeping the NHS in public hands and funded than he did Labour!
One of the reasons for John Moore's career stalling was that as Health Secretary he kept health funding level in real terms for a year rather than increasing it.
John Major would be a more realistic one; or if Cecil Parkinson or Norman Tebbit succeeded in the late Eighties.
It would also necessitate an investigation as to what form the NHS would take afterwards ("privatization" applied to the NHS tends to mean virtually anything to do with the private sector). A US system would be very unlikely; a continental "Bismarckian" system would be far more likely, probably a German model.