OP, as far as I'm aware none of the schools suggested will help.
GDST schools only offer bursary from 11+ , same with Jags and Alleyns, maybe someone can contradict me, but never heard of bursary for under 11's for these schools.
Eaton House the Manor only goes up to 11 for girls and main entry is 8+, so not much help to you.
I'd try Latymer Prep, LEH, City Junior, but to be honest although they all offer bursary for under 11's ( I think) entry at 10+ would be occasional place entry and very very rare. And everyone wants to go to these schools, so hardly easy to get in.
Also be aware most bursary at any age is usually 10 or 20%, even if household income and assets qualify you for more. Even the schools with deep pockets , it may be 50% max, and that's with a talented child and compelling case.
If you can hang onto 11+, you can apply anywhere.
Whitgift give big bursaries so you could try Old Palace, any of the GDST schools in the area like Croydon , Sutton and Blackheath, St Dunstans, the Dulwich schools.
If you're in SE London, don't forget the great grammar schools like Wallingtons and Newstead which are academically are up there with any private school and will cost you no fees.
I'd be tempted to invest in tutor and go for great 11+ results and try grammars and local Indie schools , as any bursary application needs a child doing very well in entrance tests and giving a great interview.