rabbitstew
The nearest girls-only senior school to me is around £12,000 per annum. But this includes all-day care until pretty much 6.00pm with all the drama and sports thrown in (extra for music lessons).
The local co-ed secondary school which apparently did get out of special meatures and is now "satisfactory" spends roughly £5,500 per pupil... which seems to be the going rate for secondary schools in my area.
If you add up after school care on top (that doesn't quite offer what the private school above does), it would come to about £7,500 per year. I guess the difference is what provides the added value, which is £4,500. This probably gives you good drama teachers, sport coaches, etc. - and of course, the grounds and playing fields maintenance.
So in general, instead of paying £5,500 per pupil, the tax payer would have to fund an additional £6,500 per pupil which is more than double.
With regards to boarding with regards to happygardening - I prefer her spending that money on her DS than on pretty Laboutins or the latest car. My college at uni charges around £5,500 per year for accommodation these days (term-time only) with full catering (and cleaner, etc.). So remrkably similar to a boarding school, but these are people who are 18+. No school nurse that needs to be around. Not necessarily a fully-fledged housemaster either.
You then have to add to this the fact that the boarding school will most likely pay a higher rate insurance policy because so much more can go wrong on the grounds, the longer a kid stays there... and loads of other factors associated with kids staying over night.
What ever is the difference between the total of the above and the boarding school rate will be the cost of educating the kid at a well-known establishment which most likely will have other things to offer on top of the private day school, which I have not thought of yet...