Hmm... make sure you are properly comparing the two scenarios. For example, if you didn’t do private school, would you REALLY save every penny of that for your DCs? You wouldn’t be tempted to go on holiday or have a nicer lifestyle yourself and put away only a half or a third of that? So maybe the proper comparison is not private school or enormous house deposit it’s private school or annual foreign holiday and medium house deposit.
Secondly, even though 250k sounds enormous, you’re factoring inflation for the school fees but not for houses. With growth of just 2% p.a (and it’s often a lot more in housing market) that 250k in 20 years is only worth about 165k in today’s money. Still a lot!
Finally, there are a few factors to take into your account for your DC. One is earning power - will a private education mean better a levels, better degree, more high earning job? This has been discussed above but you could look at the stats.
Second, is there a happiness during childhood point for your DC? Our local secondary comp is notoriously overcrowded with worrying ofsted reports. But if you think your DC might prefer state, it might come down the other way.
Also compare facilities and clubs/sports: these are often (not always!) better in a private school. As a pp says you can top up a state education with extracurriculars but these can be expensive and may require your time to research and to transport your DC to on weekends or evenings which is your valuable time.
So... lots of factors to consider!