Hmm, we had this last year. This is a personal opinion, but I think part of the (luxury) problem with London is that there are so many schools available within a reasonable and "not very unreasonable" commuting distance, that it is possible to overthink schooling options and come up with something which is fab on paper but a pain in reality.
DH and I both work full time and - again, personal opinion- finding the bandwidth for two separate schools in different directions would be a real challenge. The synergies of having them both at the same school is quite large. Mine travel entirely independently on public transport, but that part is not the problem: you would be surprised at how often you have to go down yourself or do pick up and drop off at odd hours (the 5.45 am start for a day trip to WW1 battlefields was a particular favourite). Also, you know when you look at things about prospective schools that make you all glowy, like "sport is for everyone"' "the school is a strong community", "we encourage every child to try new things"" and "the pastoral care and parent/school communication is excellent"? All of that points to participation and that means your moderately untalented child will be in the E football/netball/hockey team, in a massed choir/being a spear carrier in the school play and you will be constantly invited down to the school for talks on drugs/sex and relationships/drinking etc. All of which I actually think is very good, but in my experience, a good secondary school is not quite the "hands off" regime you are led to believe.
So my tips, in order: go for the same school; failing which go for two but ones that are not in opposite directions (and, critically, check out games fields as they are the killer), and failing which have children with no particular extra curricular talents at a "we only celebrate winners" school. Or be prepared to do a lot of shuttling!
(Oh, and my DC have an unerring instinct to be "besties forever" with classmates right on the other side of the school catchment, which widens your routes out further again).