People paying to send their kids to public schools remove the burden on state schools (while still paying for those state schools).
People paying for private health care remove the burden on the NHS (while still paying for the NHS).
Penalising people for doing this would be a remarkably stupid thing to do, particularly as many can barely afford them as it is.
Particularly if they were also having to take an income tax hit as well.
If they're taking an income tax hit they're on about £100k a year and up. What they spend that on is absolutely up to them but there's no way they should be getting any subsidy on VAT while the junior doctor pays it on everything they can afford.