There are loads but state school options will be very limited unless you have a faith.
Coombe Girls is very sought afte and Ricards Lodge increasingly so. Both have reciprocal sibling policies which will make them more difficult to get into unless you otherwise live on the doorstep.
Ursuline is difficult to get into even if you are Catholic (but aren't a very regular church attendee). St Philomena's (Carshalton) is another R/C option although again super popular. La Retraite in Clapham could potentially be doable in an hour (bus to S Wimbledon and then Tube).
Grey Coat Hospital School is a faith school isn't it? CofE? There's also Lady Margaret's in Parsons Green (again CofE).
Burntwood (in Tooting) has quite a sizeable number of girls going from Merton. Reasonable transport links from SW20 (57 and 131 buses and then a shortish walk).
Local super-selective grammar schools (for the very bright) are an option. Tiffin Girls (Kingston), Nonsuch and Wallington High School (in Cheam Village and Wallington respectively).
Quite a few GDST schools that would be accessible. Wimbledon High School, Sutton High School, Putney High School for Girls. Also Surbiton High School (which apparently isn't GDST).
Lady Eleanor Holles (Hampton) is another option, very competitive to get into but popular locally.
Sure there are others that I've overlooked, particularly more into London ones that I'm not aware of.