Reviving this thread because I had the same need again recently and was given a solution, which I'll share in case anyone else is interested...
I went to a gig at the Shepherd's Bush Empire, after work so had my bag with me, and it was only when I got to the venue that I learned of their no bags policy.
Fortunately, the security were able to recommend stasher.com - basically, a network of places like hotels and shops that offer a left luggage service at very reasonable rates (about £6 per bag in total, including fees).
https://stasher.com/Some of the places listed don't open late but there are plenty that are 24/7.
I used it again last night for a gig in Hammersmith, at the Apollo - I'm wise to these bag policies now so thought to check their terms beforehand. As it happened, they seemed a lot more relaxed on the door about letting people in with bags so I might have got away with it, but actually it was much better to be unencumbered, especially as the venue was heaving.
There's also a service called Bounce that I haven't used but looks very similar (even down to the web interface) - probably should have checked it yesterday because they have a location that's even closer to the venue than the place I used.
https://usebounce.com/I don't know if either of these existed back in 2022 when I was looking before but they would have been perfect.