Most of the kids I know in that area go to St Barts or Eliot Bank, and love both. I don't think I know anyone who put KG down as a first choice (despite it being closest in many cases).
The one person might know who has kids at Adamsrill really didn't like the early years, and didn't feel she was supported with issues at all.
St Barts is a funny one. The last few years there have been a LOT of siblings, and kids who I know who got in a few years ago now wouldn't get in at all. The area they have taken from has shrubs (though I do know several people who have taken the religious route successfully in the last 2 years). All.of this said, it's a very low birth year (as was 24/25) so who knows.
Most of the kids I know who didn't get St B went to Eliot B (and some chose one over the other) and rave about it. Not sure what the current head situation is, but that was the only concern at one point (think it was resolved?).
KG has a funny reputation. It's bigger than most local schools, and, because of this, often has a much wider range of issues and much more diverse population (reflecting in the results). It also attracts a lot of children with SEN issues (diagnosed and undiagnosed), as they are better equipped to deal with it them. The head has an amazing reputation as someone who works tirelessly.
I know 2 kids who are there (one didn't get St Barts, the other transferred after an awful experience elsewhere) and they enjoy it, but remain on the list for other schools. The perception is that it may not be right for others, who could get lost.
It's worth asking on the SE26/Se23/Sydenham Facebook groups (I no longer live in the area, but they are v busy groups and won't hold back on opinions!).