So one year left for one kid and two for the next?
Child 1 (current Y10) will be in Y11 in 2025/26. Fees cost = £A including uplift for VAT & price rises
Child 2 (current Y9) will be in Y10 in 2025/26. Fees cost = £B including uplift for VAT & price rises
Child 3 (current Y5) will be in Y6 in 2025/26. Fees cost = £0 if in State. Or £C including uplift for lower fees & price rises in primary.
Total expense: A+B+C
The following year 2026/27
Child 1 in state 6th form. Fees cost = £0.
Child 2 in Y11. Fees cost = £B
Child 3 in Y7. Fees cost = £C
Total expense: B+C
20% VAT on both < £A from 2025/26
0.6 x £A is surplus/reallocated to household budget/pays for that holiday.
The following year 2027/28
Child 1 in state 6th form. Fees cost = £0
Child 2 in state 6th form. Fees cost = £0
Child 3 in Y8. Fees cost = £C
Total expense: £C.
There is no way that 20% VAT on one set of fees (£C) is as much as two sets of fees (£A+£B) including VAT.
Or, if you want to mess around with formulae,
£C2027 < (£A2026 + £B2026 + £2026) < (£A2025 + £B2025 + £C2025)
£C2027 < (£0 + £B2026 + £C2026) < (£A2025 + £B2025 + £0) if state primary or private primary fees are lower than secondary fees.
£C2027 < (£B+C2026) <= (£A+B+C2025) if private primary.
Lower school fees in secondary also tend to be lower than upper school secondary. Which could represent more money to go back into the household budget. It's unlikely that your household income will decrease by an amount sufficient to wipe out all of those gains from a reduction in costs and to absorb non negotiable expenses (ie, bills).
At most, you're maybe looking at maybe a couple of holidays to knock until after the second completes A levels - so two.
I'm not taking into account university maintenance for 2026 or 2027 as you'd have to do that whether child A (and B in 2027) are in state or independent. Or maybe they take out a student loan instead of being fully funded. Or maybe one or both do Gap Years and work. And they will have both likely graduated by 2031 /be working when Child C finishes Y11.