I've skimmed the whole thread. I agree with everyone about food, clothes, activities, trips, etc., notwithstanding shedloads of clearasil, hair gel, Lynx, nice bubbly bath, etc
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From the other side OP you also say your dc do a lot of lovely activities and go to private schools as did/do ours. So I think there are some other things to consider actually - not least the expectations your dc will pick up on as they get older and it just grows and grows as many posters have alluded to.
When DS started at prep his fees (London boarding were about £11k per annum, when he finished at 18 they were closer to £19k - similar pattern for dd who will transfer from reasonable gdst school in September to less reasonable Surrey public school [we think] for an extra £5-£6k for 6th form). The demand for state of the art tech does rise, are you aware that a flute fit for grade 7/8 is presently over a thousand pounds. Add in sports or music tours - it is very difficult when your child is "selected" for such a tour at £2.5k a go to say no (we did say no for the biology trip to the Galapagos Islands for £3,900 and still dine out on that one). DS has been on three such tours and is currently gapping in NZ - guess who pays - and believe me there is an innate expectation among parents in the indy sector that all uni costs will be absorbed - "ha, cheaper than school fees at £20,000+ - I hear that regularly". So, £36k of unbudgeted uni fees for two. I even actually know a family who switched from a BMW to a Merc to fit in their dd's harp
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In the indy world it is perfectly normal to expect to pay for: gym, drama class, sports club memberships (external to school), horse-riding, school trips (allow £4,000 a year for two), phone contracts (good phones), teeth - you would be amazed how expensive perfect teeth are when they are good enough vis the NHS, contact lenses, highlights, festivals (Reading, etc), ghastly trips to ghastly places in Crete and Spain which are a rite of passage, dalliances with thinking they might go to uni is the States. Driving lessons and a tiny, ancient car, shared with mum to get insurance credits are minimalistic in comparison.
I'm quite sure more will come to me. Oh yes, dd wants to be an actress and we have said we will fund RADA - first she wants to qualify as a doctor. We have said fine; providing you get some prof quals under your belt first in the hope she comes to her senses
For the record, ours aren't even awfully wanty. DD isn't interested in Uggs or a tiny diamond stud like lots of her friends.
It's all worse for us because this world was alien to DH who was dragged up around the corner from the local comp and remembers being hungry. As far as he's concerned the £8k on three sports tours has been worth every penny for the experience it has given ds and which he didn't have and would have preferred to a shared sandy ice-cream cone in Brid.
I think if you have to ask if you can afford a third child OP the sad answer is that to keep up the sort of lifestyle you have now, probably you can't. I'm sorry to be blunt but what will you do is times get tough - it's much much harder for a child to go indy to state than vice versa I think.