We have just started at NP and are basically happy with how things have gone so far. Thomas' did not make our shortlist as it seemed very pushy and more conservative, and NP felt more open; however, we have found it to be more pushy than it seemed at the open day. I think all the independent schools are demanding of their students in this way. All the other parents I've met absolutely love it, fwiw.
Can't comment on the 11+/13+ thing, as being a foreigner all that is far too bewildering for me.
Children come from all over SW and central London, from Wimbledon to Balham to Chiswick to W1 to Cadogan Square. We have not done playdates (c.f., being a foreigner, and not understanding those either) but in good weather half the class surges into Battersea Park and children play together there.
It's not hard to get to as there are two train stations beside the school as well as lots of bus routes. Getting the car in on a school morning might be a bit more difficult, as all those Range Rovers take up a lot of space....