My DD was in a position (of her choosing, though she did find it daunting initially) of not knowing anyone in her secondary school this term, and it's turned out there are a couple of girls she's friendly with who do live near us, which is more than I'd expected. At her school there were quite a few who'd come from the same primary schools and she did find that inhibiting at first, but she was far from the only child in the same position, and that helped.
The London Schools Atlas is an excellent resource, annoyingly not updated for a couple of years but a useful ready reckoner as to where kids at each school actually live (it maps addresses onto defined postcode areas that LAs use for planning). That will give you a heat map for each school, and also which primaries send most kids there.
Of the three you're looking at, HPS will inevitably have the tightest group of kids living near the school and having been to primary together. Faith school intake tends to be more disparate. It looks like the majority of St Michaels girls live in north London (unsurprisingly) and GCHS in south, presumably because if people are further north they're more likely to opt for Marylebone.
It's been said on these boards many times, but going up to secondary with existing friends is only useful up to a point, most of my DD's primary year went to our local school and have already broken free of their previous groups, only still hanging out with one or perhaps two closest friends. And that's after just half a term!