Not from your area but, remember there is, of course, a cost associated with all secondary schools - not just private ones - and it can be quite a surprise to some parents as to how much the little trips here and there, contributions to this and that, unifrom/kit etc all add up to, just in a "bog standard" comprehensive or Grammar School. Obviously you don't have to go on all the trips but there are some which are more compulsory - as they are the curriculum based ones (broadly speaking these take place in the school day and are directly related to the school curriculum, as opposed to a sports tour abroad, for example.)
My brother in law has three children at various private schools in the South East - he has always, always lived by the rule of thumb that for each child at private school he budgets the equivalent of at least a full term of fees again, annually, to cover the incidental costs/travel/kit/extra curricular/any meals/exam costs etc. (All of his friends do the same - but I appreciate this is a small sample!!) That is, if the termly fees are £4000, then budget £16000 for the year. If you have to use private school buses, they can be quite significant costwise (which he does). I know you will now get lots of people on here saying "oh we don't pay that, we only pay tuppence ha'penny" and that's great for them, but you asked for a rule of thumb and this is what he and they have said. Better to be over cautious and possibly have money back!
For info, we have boys in GS, for one boy, bus fees are £750 a year (and rising), uniform costs (at start) were around £400 including specialist rugby kit (for eg a decent mouthguard is about £40) trips we budget around £500 a year (battlefields trip to France this year which is a curriculum tour was about £400 and other day trips - next year Iceland, non compulsory is £1000 etc etc), we do packed lunches rather than hot dinners, we pay for the occasional text book/magazine (for the older boy), things like DoE are obviously additional....but it does add up - for us, easily £150 a month in a state school - but we try and let them access as much as they can...
Some state schools are less than that, but maybe don't do quite as many curriculum trips and certainly not as many non curriculum trips. Others are better funded, or have pots of money from Governors, PTAs, Benefactors that help shore up the costs. All I am trying to do is remind you that whilst there is a cost to private school there is ALSO a cost to state school so the private school costs will likely be higher but not necessarily hugely higher! ie I know it sounds frightening to say "budget another terms fees" but when you break it down and look at uniform costs, travel, trips etc, it makes far more sense as to why this might be good rule of thumb...
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