Tiffin has an inner and outer (designated) area of catchment. No girls have got in from beyond these areas since they were introduced, as far as I am aware, though living outside this area doesn't stop you applying. Designated area postcodes are:
KT1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 17, 19
TW1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17
SW13, 14, 15, 17, 18, 19, 20
W3, 4, 5, 7, 13
SM4
CR4
You won't find any schools where sports are not compulsory, but SPGS has a good range of different things available including things like dance and yoga. They get some choice in this as they get older. DD is not even a tiny bit sporty but she has mainly enjoyed her sports lessons apart from the ball sports which she was never going to like anywhere as she struggles to catch a ball reliably. Lacrosse is awful for the unsporty, though I imagine hockey is almost as bad.
You probably need to look at what individual schools are offering in terms of curriculum etc to see whether these schools are going to be right for your daughter. For us, we wanted the very rich foreign language provision that a private school offers. If I'd had a more maths/science loving child I would probably have been just as happy with a good state option as they will also offer triple science. They won't offer the ability to do so many languages or so much choice in which ones, and this differs between private schools as well. Some schools might make a humanity compulsory at GCSE. There's a lot of variation in what is available.
Also, your daughter's personality will make a difference. DD came from a state primary and was sick of being an outlier. She loves not being the best at everything and having peers (and people who are better than her) in the academic sense. Other children may thrive on being a bigger fish in a smaller pond and get discouraged if they are not always near the top of the class.
As others have said, SPGS is very very liberal and what rules there are essentially boil down to 'be sensible'. What discipline there is seems to be aimed at getting the girls to take responsibility for themselves which very much appeals to me (the whole point of this parenting business is working up to children being independent and confident, really). DD enjoys being treated more like an adult and has responded well to this approach. I don't think she would have thrived in a heavily rules-based environment. She would have spent a lot of time railing against injustice, I think! One of her friends is at Ibstock and DD was outraged to discover that they are prohibited from attaching keyrings to their bags (presumably because the jangling is annoying but DD is appalled at such a curtailment of liberty).
I don't think they work them incredibly hard at SPGS, at least in the lower years. DD gets very little homework (usually much much less than an hour a day, usually about half an hour or so, a bit more at weekends) and has not struggled to fit it in, even with music practice in the mix as well. They don't seem to set homework for the sake of it, only if there is something useful to do. One thing to take into account is that the school day is longer at SPGS than at many other schools and once you have added travel on, it can be a really long day. DD was shattered for most of her first year but is getting the hang of it now. We do live further away than you, though.
There are some very rich children there but equally a fair number from more ordinary backgrounds. DD's closest friends are mainly not in the super-rich category! They mainly seem pretty normal to me (I am also not super-rich).
If you think you might be eligible for a bursary, you should contact the schools directly and ask what you might be eligible for. They will be happy to help.