Having spent the best years of my youth digging in the caves of the Avon Gorge, I am still wondering how we failed to find the master cave. It could be that we were digging remnants of caves exposed by quarrying or by the down cutting of the gorge in ice age times. If it is the latter case, then the master cave was destroyed when the gorge was formed.
Another factor is ?Vertical Range?. If you look at Swildons, Eastwater, Cuthberts etc. The Vertical Range between the swallets and the resurgences is about 700 feet? In the Durham Downs / Avon Gorge case it is about 200 feet. Unfortunately Durham Downs lacks any active swallets. There are plenty of shakeholes, but most of these have been filled in long ago.
Even the Storm Water tunnel failed to breach any open fissures, ditto the railway tunnels. I know that this fails to answer you question, but as Fred Davies say ?Caves is where you find?em?. Sadly, not in the Avon Gorge.