Ha, well, there you go. My gym membership went years ago as I couldn't afford it given the school fees (and didn't have time to go, anyway). We've never owned a car. We have one week in Europe as holiday each year, but it doesn't cost £5000! Just as important, we both think carefully before spending money on anything. I'm often shocked at how much money other people spend casually - and, tbh, I used to too. Books when you read a good review, coffees out, extravagant presents, magazines, takeaways - I don't buy any of that stuff anymore. It adds up. DH and I both have our indulgences, but they are carefully weighed for being the most valuable they can be. We buy good wine and drink it at home, but seldom eat out. We buy vegetables and fruit that are in season where possible, take advantage of special offers, eat a lot of vegetarian meals. We live in a flat, and mortgage payment even with a bit of overpaying comes in under £700. Even, we have just one child, partly because we always thought paying for private education might be important to us.
We're about to commit to boarding school fees (so our fees for one DC won't be so different from yours for 3 at day school!) Our earnings are about the same as yours, OP, but because we're academics and already at, or close to, the top of our relative-to-some poorly-paid profession, have no prospect of significant increases ever, and our previously-good pensions are about to be ruined too, grr. The way fees go up and our salaries don't is a concern: we could do it if everything stayed the same, but only just. It may be that we get a small bursary, or at least bailed out if things go pear-shaped, because of this. Not counting on it, though.
The way I look at it is: the fees are less than my salary, and plenty of families live on less than DH's salary. So how could it possibly be true that we couldn't afford it? It's really just a question of how much we want it.
Sounds as though we may want it more than you do, and that's OK.