This is what I've been wondering, if the NHS went private would we pay 20% less tax? I highly doubt it.
You're right, the answer is no. The cost of the free healthcare that we would still need to provide (a lot more limited than now, like the US) would go up considerably, due to economies of scale, and then the reduced NHS paying private companies for space/ gear/ consultation that they no longer can afford/ have in stock/available. It wouldn't take the full 20% but probably 10% plus.
Then couple that with the social problems that people not having healthcare would lead to (like how lack of social is F***ing healthcare now), it would jack up social care costs. My bet is that would sap the remaining 10% instantly. Social care is already completely wrecked and needs a pay boost, so that 20% would end up 10% going to reduced NHS and then probably the other 10% being diverted to councils to help with social issues. Tory's wouldn't do this mind (the 10% would get lost to the rich somehow), and things would get way worse, but Labour would, they would have to for the 2025-30 term.
Then obviously couple that with a "more sick" workforce, being less productive, worse for the economy, it would mean we need to fund other areas with tax to make up for that, as they would be raking in less tax from other areas/ profits etc. I think the current workforce is already at record sickness levels, largely as it's older and from the tail of the pandemic, and we can't afford people not getting checked out when they're ill, as they're worried about cost/ insurance etc.
Obv the private system goes on the assumption that everyone can afford private healthcare too, and still paying out the same income tax as now. Can people afford another £200 a month each, after this massive inflation? It's not going to happen, most on <30k or older than 60 (and certainly pensioners) would struggle to be able to afford it. Less people going private, means the cost for those who can goes up, again economies of scale. IF there's no NHS backup then private goes up. There would be no £200 a month insurance if it had to cover what the NHS does. It's like a bad negative feedback loop.
The last thing we need is more people sick/ leaving it ages to get fixed up, and longer waiting lists etc. A healthy workforce is a productive one, and 2% out of a productive 2bn is better than 3% of a non-productive 1bn etc.
What is interesting is that the Tories rely on the older vote, generally people who have accrued money over time, and a lot of them have moved over from Labour (not many are born a tory etc). Effectively they become selfish and want to retain what they have earned, i.e they want payments from others when they're skint (understandable), but when they have money themselves they want to keep it, and not help the worse off (not realistic), they want both sides of the coin. The Tory assumption is that the older votes are easy for them to retain (works better when the NHS does), but an older population is a more sick population, and if there's no NHS then their selfish voters will look at what would serve them best, and that's what will keep them alive. Money is worthless if you're going to get wiped out by insurance costs or die from something you would have normally survived.
It's interesting and I've only just realised that it's labours fighting and help with the NHS, which has given Tory voters an insurance policy to cover the boomers. If we had no NHS it's unlikely the tories would have had power for as long, as they're now going to discover by wrecking it. This could be the big tipping point which moves more older voters to support Labour, as they will know the Tories will not want to keep the majority of them (those not ridiculously rich) alive. Tories have zero interest in really old people with no money, or those whose money will get sapped by care costs, they end up a massive burden and when they get really old they stop voting, or may move back to labour when their cash runs out.