OP, I have a lot of friends who were privately educated and very open about it.
What became glaringly apparent whilst interning in London was that ‘secondary school’ was important but prep obsolete. I was often asked ‘so where were you educated?’, it was only ever in reference to secondary and my obscure ‘non posh’ northern school was often met with a look of confusion 😂🙈.
I would advise that unless you’re aiming for a big name secondary school, Eaton, Harrow, Marlborough, St. Paul’s, Westminster, charterhouse...etc there’s very little point in attending a private prep school and your money would be far better saved in preparation for (18,000 a year day/£30,000 a year boarding- and all of the other expenses which come with)
Equally (I don’t know your financial situation) but unless you’re able to fund private secondary education it’s absoloutley not worth it to attend a private prep. It’s unfair to the child, a good friend of mine did this and was then dumped into a struggling local secondary school at which point she simply didn’t fit in and was awfully bullied.
If I were in your situation (and moving we’re not an option) I would have DC attend local primary whilst investing in a very good tutor (especially in music/ a language).
Being state educated may even go in her favour during the secondary admissions process x