Huge congrats on the Tiffins offer - that's no mean feat! We're not sitting 11+ until next year, but my understanding from open days and talking to existing parents is that all these top schools have girls coming from far and wide. Just look at the bus network for LEH - it's an enormous geographical spread. Or ditto the map on the CLSG website of where girls travel in from. And I know SPGS says you have to be within a 1 hour journey time, but that still means you have some girls coming in from Golders Green and others from south of Wimbledon - they're not easy socialising distances. I have asked the question (of both girls and teachers) at many schools re socialising, and the feedback I've got is that very little happens during the week, or even at weekends in the earlier years, as they're all so busy doing a million extra curricular activities. And by the time their socialising at weekends, they're perfectly capable of getting on buses / tubes / trains to do that independently.
I think 45 mins is pretty standard travel time for secondary schools (though of course it all ultimately comes down to personal preference, esp of your DD as she'll be the one doing the travel for the next 7 years). I would be genuinely astonished if there weren't other girls from Wimbledon or the surrounding area at Tiffins. At least Tiffins has an inner and designated catchment - unlike Henrietta Barnett where girls really are travelling from half way across the country - so the geographical spread is at least a bit contained.
But if you want a school with a local feel, and your DD wants to have most of her friends be local, then Tiffins probably isn't the right choice.
From everything I've heard though (and we have friends in Y7 there at the moment) it's a fantastic school, and of course free!