Its a bit unfair comparing grammars that cost zero and are state funded to schools that charge around 30K+ a year and have huge charities /trusts/guilds behind them with warchests in the multi-millions, (i.e Mercer for St Pauls schools and Bute)
So while Grammars can select, they can't fund the sort of added value the private schools can.
Schools like St Pauls ARE more selective than say Henrietta Barnett School, Henrietta just demands clever girls, St Pauls demands clever girls who have welahty parents, bar the tiny chosen few on generous bursaries.
OP, everyone says this , state till 11, we'll apply for grammar or Indie at 11+, believe me, if you're worried about prep fees, they are nothing comapred to senior school fees and 6th form, and grammars are HUGELY oversubscribed in London, or anywhere else if they are good, less stressed is not what comes to mind.
But as @TizerorFizz says no good state primary is going to come close to a good prep, in facilities, in one to one teaching, in activities, trips, sports, clubs, music, library, teacher and TA ratios, in progress reporting, and for me that was most important because the 5 to 11 years are so vital in development.
I don't really care about feeding to 'top schools' I want well rounded kids at 11, who have enjoyed a full education with great facilities.
I could happily send all DC to prep then state school, knowing they had a great foundation, the irony is state comps that have streaming, as most do, are fantastic for bright middle classed children, whereas a lot of parents send their DC to overcrowded state primaries with a tiny library or no library, and then cram them to get into grammar or private senior where they are catching up with the kids who feed from preps.