I live on the Battersea side of Clapham Junction, there's a leisure centre on Latchmere road with courts.
Lo and behold, if you haven't discovered, there's a club that runs at the latchmere road place on Sundays - 12.30 til 2.30, though often the times are pushed more like 12 - 3pm. Fair old trek to the sports hall if you go in the main entrance, was hard for me to find it first time. They have swimming pools and other stuff too. £7 per time last I went there (unsure about membership or if casual is only option/if have yearly rates), intermediates upwards (beginners not very welcome), play with feathers, 5 courts I think (at least 4, maybe only 5 sometimes depending how much else is booked privately or maybe Im just assuming too much from what I guessed from my couple of times there).
I was a bit out of practice, am intermediate-ish usually, when I went and they gave me a fair few games but one of the organisers suggested I have some more training before coming along more. So I think many club-level players, probably a few county-ish (just a guess..). But they did suggest where to get some coaching!
Btw, I haven't been in a loooong time but hope and expect its still going strong. Not as easy to get to on public transport as many other clubs Ive been to.
Currently go to several meetup.com badminton clubs around South-West or central london, fave social-wise being elephant and castle one at south bank uni "london social badminton meetup" on every sat. at present, usu. 3-5 but can vary. That group only play with plastic though, a completely mixed group from beginners to higher level intermediates; much less cliquey than any other groups I've been to, you are expected to mix in a bit so sometimes you'll play with less experienced folk though its very casually organised and you can pick the games you want. Sometimes the better players are a bit cliquey but mostly very friendly and not so, the good players will give you a game if you're inexperienced and team up with someone ok.
They also do coached sessions very occasionally, mostly for absolute beginners to help with basic shot techniques.
Other meetup.com groups vary, some are similar, others use feathers. Check out gumtree sports section too, advertise for games or look for other regular ones. Theres one I went to a couple of times that only had one, maybe 2 courts at most, but played decently and with feathers and cost wasn't that bad - they had about 4-6 people per court.
Most/all the meetup.com groups expect you to play doubles the majority of the time; I don't mind..
Looking for guaranteed singles games from the above mentioned ones? Tough choice.. No Strings badminton (with various groups, and more to come in September apparently) I think is possible sometimes, or near the end when folk are tired/some have left from the meetup.com groups, there is a fair chance if there's enough courts at the time and not too many people.
Hope that's all useful! I checked out about 4 or 5 groups I found online when I moved up to London and fancied starting playing again, and only went once to most of them til I found meetup.com as they were too picky/not that friendly.
I think I know where the comment about 1 court with very low beams/ceiling (that they play a let for mostly) was from, played there once (a school's court, wandsworth-ish?). Also very very stuck in their clique, and the low ceilings were just too much pain. They also expected me to be very good without indicating any skill requirements when I spoke to them on the phone beforehand, and were miffed when I didn't match up to (uncommunicated) expectations.