Whilst on a bus I went past a place called Flip Out and saw an advert for caving. So I later googled it and found Flip Out is a nationwide "trampoline, adventure and inflatable" parks. The branch in London E6, at East Ham, near Barking, has "London’s first 100 meter Indoor Caving and Potholing Experience (Seeing is believing)". I couldn't find any more on their website, Flip Out London (E6).
However I did find an article on Boxedoff, "London’s first indoor caving experience set to open in East Ham in spring". [2019??] The part relevant to caving says "Plans to open London’s first indoor caving experience in East Ham have been announced.
The 100 metre indoor potholing experience will form part of the new Flip Out London E6 trampoline park, which is set to open on the site of the former Granada theatre on Barking Road in the spring.
The indoor caving experience will give adventurers the chance to explore a network of twists and turns in the deepest darkest corners of the underground cavern, which will be located at the new Flip Out trampoline arena.
As part of the indoor caving experience, explorers of all ages will be challenged to choose the right path in order to reach the end of the cave."