You get more at private school for your child, but if you pay 15K+, what other answer can one expect??
Private pre-prep ( 5 to 7) will be by and large the same as state primary- work wise BUT smaller classes, more one to one, lots more clubs and after school and breakfast club places. You'll have swimming every week at private in Reception, and usually one 'in house' musical intstrument lesson , better sports, a music teacher, and a language teacher. You'll have much more parents who are pretty much obsessed about achievment and getting ahead, as they are paying an arm and leg on fees and want something in return.
Things start to pull away at Prep, (Year 3) from state primary and all these things above start to pay off in producing more 'rounded ' kids , more confident - huge generalisation as private schools are full of kids with parents with wealth, who own their own home and can afford culturally enriching lives, these kids are confident in a state school or private school. Kids that are a bit 'meh' benefit from the extra 'care' at private school and bright (and average) kids don't get as bored as they can at some state schools.
After Year 3, able children are given opportunity to pull ahead and prep schools aren't chained to government targets, etc, but you know this if you've ever taught in a state school.
If you're happy to supplment with swimming in reception, language online classes, extra clubs like ballet, junior tennis, etc, music instrument lessons, you can 'recreate' a private school experience for your child, but its bloody hard work , I know a few parents who do it, and its a 7 day a week job, compared to writing a cheque and getting the school to do all of it for you Monday to Friday and having weekends free.
Also if you're aiming for grammar, prep will make it easier to get into one.
Anyone who says 'its a waste of money' is simply lying to themselves, a great prep school towers over a great state primary, the spend per pupil makes any comparison meaningless like comparing buying a 300K flat to a 900K house.
Quote from Institute of for FIscal Studies:
'In 2022–23, average private school fees across the UK were £15,200 in today's prices (net of bursaries and scholarships). This is £7,200 or nearly 90% higher than state school spending per pupil, which was £8,000 in 2022–23 (including day-to-day and capital spending).'
ifs.org.uk/publications/tax-private-school-fees-and-state-school-spending#:~:text=In%202022%E2%80%9323%2C%20average%20private,%2Dday%20and%20capital%20spending).