Hi
I can only help with advice on a couple of these schools although I have no direct experience myself (DS is secondary school age) but do have friends with DDs currently at some of the schools.
Ricards Lodge is definitely on the 'up' with a much, much more visibly middle-class demographic of girls in recent years. I think if you look at any of thes pan-London maps which show where children at a school come from, you will find the catchment area for RL is shrinking year-on-year to the point where all the girls will be Merton or Wandsworth-based. I think it's very good for girls with a leaning towards drama, art too. I have friends with discerning standards who are happy with how their girls are doing there!
Burntwood seems to have a very good reputation, particularly in the sciences, but in recent years seems to have attracted an increasingly Muslim intake. That isn't of course a problem in itself but it might have an impact on out-of-school friendships etc...I'm sure I read somewhere that this demographic of girls accounts for some 70% of the total!
Tiffin Girls is quite different from the other schools you've mentioned in that it is an extraordinarily over-subscribed super-selective grammar. We have known some very clever boys who've got into the super-selective grammars in Sutton/Wallington BUT have never known anyone get into the Tiffin Schools. It is an extreme long-shot and not an option to be taken lightly.....
Greycoat School - my information is out-of-date as I had a Uni friend who had been there (she was a vicar's daughter). But I have perused the school website (idle curiosity) in the past year or so and got the decided impression that it's highly unlikely that one would get a place unless living on the doorstep or from a very church-attending background. Is it possibly the C&E equivalent of St Philomena's in terms of difficulty of gaining a place?