I'm in the area and have one at Blackheath High and one at Balckheath Prep. Generally, BH is probably a 'kinder' school, easier to get in too and has done wonders with our dd1, who has has to work very hard to catch up with her peers. BP is much more selective and a more pushy. I am presently in two minds about it, but it does get good results if your child buckles done. They don't seem to deal with anything out of the ordinary as well.
BH Senior is really improving as the Juniors are presently piling at least 75% of year 6 into the Seniors so there is a much more co-herent strategy thru the school as a whole.
I looked at Invicta and also James Wolfe, but frankly they were back ups for us, if we didn't get the Prep place. They were both good though. I preferred Invicta.
All Saints has a great reputation, but we are both non-Church goers so a bit of a no-no for us.
You should also look at Colfe's in Lee Green as great site, bit of change recently at the nursery/KS1 level, but you should consider.
We went to Pointers and Heath House - both too dependant on individual heads/owners for my liking....
Good Luck.
Come along to a SE meet up and chat....