Apparantly the bethnal green cavern is close to the location of the
deep level shelter/bunker, nearer liverpool street, but past the
sidings. I know that when I've gone that way, there is a small gap in
the tunnel wall on the inside of the line in a location that
approximately matches that description.

The 7bis Cavern sounds cool though. Can you imagine being on the
central line in a boring tunnel and then going over a huge viaduct in
an underground cavern, that would be amazing.