OP, my view is, and has always been, that what I can afford doesn't just mean what's in my current account.
Looking at any large expenditure (which must surely encompass school fees) I always ask myself what will be the impact in one, two, five, ten year's time.
It's not tat you have a large mortgage, or that you won't be able to service an increased amount, it's more that it is a terrible way to pay for school fees. Not so much robbing Peter to pay Paul, but leaving him drugged and naked, chained to a fence in Kabul.
It's obvious to me that you want the best for your DC and have decided that a private education is top priority whatever the stakes. I almost commend you for that...
However, you need to keep in mind all the other huge expenses that are going to come up if you really do want your DC to have every advanatge. I don't know if you have friends with older kids/adult kids but the list of expenses just grows and grows.
Language schools, sports trips, theatre tickets, D of E expeditions (£200 to camp!).
Tutors, music lessons, books and exam costs (yes you pay for GCSEs in private school).
Visits to university open days, interviews.
Onceat university; accommodation costs, food, books, travel, clothes, insurance, phone contracts, internet, a laptop, sports equipment...
And what about an MA, now often an (unoffical) necessity. Hardly any funding or loans. You'll have to pay.
Or professional exams. No help with these without employer sponsorship.
And the dreaded internship(s). Young adults being expected to work for nothing, usually in a city where accommodation etc is so expensive....