It's the living on the edge, for years on end that does it for me. I've been there. I also have some friends who on paper could afford it, they thought they could cut back and put two kids through, although they were on over 100k, similar size fees, smaller mortgage. The reality is cutting back is really hard and they ended up up to their eye balls in debt.
I'd agree with the poster who said try it first. From this month take away two grand a month school fees from your monthly spend and see how it works, then factor in annual and additional costs then decide.
My child was privately educated, I only have one, and at this level of income I would not have considered it, the benefits are not enough v the daily struggle, and when she was little it was difficult at times, we may have earned double the ops income, but our mortgage was double and it was still a struggle and we argued over money for the first and only time in our lives.
We also needed to pay for childcare in holidays and not just the cost of living, but the cost of working, from clothes to lunch to transport, and when the big unexpected bills came in, it became stressful. We also wanted to do things like go out with our friends, buy clothes, go on days out, have a take away, have a holiday, but we found we simply couldn't , we had no money and that is fine when an end is in sight but for up to a decade of living like that, no, I don't think the benefits are worth the negative effect on the family.
Give it a shot and see how it goes before deciding,