Talk

St Catherine’s, Twickenham.

There is no chance whatsoever that you would get in to those state schools unless you lived very close to them, or we're confident of eg a superselective language altitude place Are you planning to move house?

There are GDST schools - WHS and PHS should both be reachable, and SCHS maybe. Or do they have a reputation for being more selective that you would want?

Depending on where you are, what about Woldingham?

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.

Sorry, just read the 'less selective' paragraph. Many of the above are very 'selective', just not necessarily academically.

There isn't actually that much choice really if you don't have a faith and have an average type of child. Catchment is generally everything if 'selective criteria' are not

Whilst I agree and don't do this - it annoying when you pick up an item then 3 isles later see something similar on a deal or half price -

Look at the Independent schools council
Web site and put in your post code or Surrey and see what you get. There are plenty.

Less selective - More House, St Augustines Priory, St James' Queensgate, Queens College.

Bar St Augustines, these are more central. Stick post codes into TFLs journey planner or Google maps and see which ones you could get to. There will obviously be other schools if you go out of London. 40 minutes journey time and one change is probably the maximum desirable.

Woldingham?

St. Martin-in-the-Fields, Tulse Hill.

Thanks for all the replies! There are schools which I hadn't heard of so will be checking them out.
I'm aware of catchment/ faith issues to get into a lot of the schools and would consider a move.
Whilst DD is bright she's no genius, I would say she sits in the middle of her (very) bright class. With odds of 1 in 7 (at least!) to get into the GDST/LEH/grammar schools, which are super selective academically, chances are she wouldn't get a place.
So before we are left with (possibly) nothing I want to try my best to have a decent back up school for her.

Marymount?

Waldegrave in Twickenham, Roseberry in Epsom - both state schools.

Rosebery School Epsom is really excellent (although massive). It has quite a tight catchment area (although nowhere near as small as for some of the very in demand London secondaries) and a sibling policy.

From hearsay Sutton High School is said to be slightly easier to get into than WHS. I know of one local family where the DDs were split between the two schools because younger ones didn't pass the entrance exams for Wimbledon High.

I'm not too sure where SW20 is, but Surbiton HS is used as a fall back by many, including those from central London. It's a big school so takes a wide ability range. Once in lots of scope for a DD to find their level. Sport is strong and girls we met, through Sport, seemed happy.

Agree Sutton is considered less selective than Wimbledon or Putney.

Visited Marymount recently and loved it but it's about £8K/year more expensive than other independents 😱 on the plus side, class sizes are capped at 14 whereas other indies like the GDST it's 24.
Didn't know Sutton and Surbiton were meant to be less selective; thanks for the tip, I'll check them out.
And definitely will look at the state schools mentioned.

Epsom College now take girls all the way through. Great school, amazing grounds but very expensive

Also City of London Freemens in Ashstead is a lovely school but perhaps a bit far?

But both Epsom and CoLF are co-eds surely. OP was asking for single sex.

I am looking for girls only but thanks for the suggestions anyway.
I have those 2 schools on my 'other' list on the off chance that we don't get a place in one of the all girls schools that we want.
Though Epsom College is eye wateringly expensive.

Just thought of another one: Notre Dame Cobham.

Central foundation girls school in Bow east london dont know if thats too far. Literally few mins from station.

Manor House has buses from Wimbledon

I live in same(ish) area, and would look at the following:

State:
Coombe Girls - depending on where you are in SW20 you may have a chance of a place, they have added an extra class this year (although sibling policy with Coombe Boys now).
Ricards Lodge - catchment is getting smaller as it becomes more popular with local families, and it has just achieved 'Outstanding' Ofsted (there is also a sibling policy with local boys school Rutlish making the catchment smaller).
Burntwood - near Earlsfield - has some selective places if you are too far away for a place (much less selective than grammars though so don't rule it out, would need to sit the Wandsworth test in September).

Church (very competitive unless practising regularly):
Ursuline High School - Catholic.
Holy Cross - Catholic.
Lady Margarets - CofE - Parsons Green.
Grey Coat Hospital - CofE - Pimlico

Independent (less academic):
Surbiton High
Sutton High - much less selective than WHS, PHS, a lot of girls go from SW19/SW20
Notre Dame (Cobham)

Hope this helps!