Couple of questions to OP.
First, how many kids are we talking about? Clearly the level of income needed is different if you have one kid compared to half a dozen.
Second, you have posted this on the Boarding section of MN, but you don't mention boarding. At most schools there is a big difference in fees for day and boarders.
I would say that at your level of income one child in a day school would be no problem at all. Four kids full boarding would be unmanageable.
In response to those people that question the benefit of private schooling, I would agree that in the majority of cases, an academically gifted child will succeed in any good school, be they state or independent/private/public. I would also suggest that where a child struggles academically, many state schools are more well equipped to provide support than some independent schools, though clearly this varies widely from school to school.
However, if your child's passion lies in sport, music or drama, I do think that this is likely to be prioritised and encouraged more at an independent school, though again there will be exceptions.
As to cost, I would say that for a decent day school the basic fees would be #25k-#30k per year, and for a boarding school #35k-#45k, so say #2k-#2.5k or #3k-#4k per month respectively, per child. On top of this I would add #200-#300 per month for extras, including trips, music lessons etc, not including big items like residential trips and sports tours. They really add up.
This is per child remember.
Apologies that my computer seems to prefer a # over a pound sign!!!
Independent school is not for the faint hearted, and this will inevitably take money that could be spent on fun family stuff, or your retirement, and there are great state schools out there.
But if it is feasible, there are real benefits from a good independent school. Not from a rubbish one obviously, and they are out there too.
Really difficult question I know, and we made different decisions for each of our kids. Good luck!