At today's rates, good private schools SE England, it will cost roughly £230,000 per child for fees alone from Reception through to A levels. You will find some for less, and some children give siblings a discount, although it's usually only about 5%. Then, all the uniform, extra curricular activities, etc, etc.
Annual fees will start at around £6k from Reception to around £15K to Yr 6, then £25-30k per year for secondary.
Of course if you're working then when you have a child you will need nursery/childcare fees from when you return to work after maternity leave.
If you 'save' a proportion of this amount in advance and put it into an educational trust fund for your DC, you will find it easier.
But then you will also have university fees afterwards, and with those incomes you will be funding it in its entirety. So budget at least another £30k per year for that. If they've been used to the great life though, I suspect you would need to provide more than that.
Or you could go state for infant school, or for the whole of primary. You could hope for a bright child that gets a scholarship, but they are often only around 10-20% of the fees, or your DH could be realistic and you could spend that money on a fantastic house in a catchment area near a great school and go State, or Grammar school.