OP, if you are looking for “academic excellence”, the schools you are looking at are not really “the best” when it comes to GCSE or A-level results. Go on the websites for each j dividual school and look at the percentage of 7/8/9 grades they achieve at GCSE (old A-A*). This is obviously not the end-all-and-be-all, but it will give you some benchmark for comparison.
The “top” girls or co-ed schools reachable from SW London areas would be the Hammersmith schools - St Paul’s Girls, Godolphin and Latymer, Latymer Upper (co-Ed); then there is Lady Eleanor Holles (Hampton); City of London Girls; Wimbledon High School; James Allen Girls School (Dulwich way). These schools regularly achieve 90-95% A-A*, but are highly competitive entrance exams, etc. Then there are schools such as Putney High and Kingston Grammar which are also very competitive. Another one now wouid be Francis Holland Sloane Square - this is a smaller school, but absolutely fantastic and in the up in every way, by the sound of it (90% 9/8/7 grades last year putting it among the “top tier” of schools).
Outside London the is Guildford High which is similar in terms of results to some of the top London independents.
All these schools will have just about anything and everything going on in terms of extra-curricular and all will claim to have excellent pastoral care.
To give you an idea, there are maybe 10-15 applicants for every place at some of the top London Day Schools, all of whom will be in the top handful from their primary classes. However, people do move and places may come up in later years so it could be worth asking if your daughter is academic. Why not?
You could also look at Surbiton High which is very popular? There is Ibstock Place near Barnes? Notting Hill and Ealing High? These schools get great results, but may be slightly easier to get into than the schools mentioned above.