This is a ventilation shaft for the Clifton Down Tunnel. The railway tunnel was opened in 1877, and is still in use. According to this page (which might've been put together by my friend Rob, by the looks of it!): this ventilation shaft used to be topped with crenellations, and also:

Clifton Down Tunnel is 1751 yards long. Halfway along its length there is an opening into a cave that exits half way up the cliffside of the Avon Gorge.

...so that's quite fascinating. I think it also used to connect to the Bristol Port Railway and Pier tunnel that I found in the Avon Gorge on another wander.

EDIT TO ADD (14 Oct 2021): I'm just reading Colin Maggs' The Bristol Port Railway and Pier (Oakwood Press, 1975) and the tunnel was indeed built for the Clifton Extension Railway, which linked the Bristol Port Railway line with the rest of the national network. It sounds like quite a feat of engineering, including the use of a diamond boring machine invented by Major Beaumont, MP: "Cutting facets of black diamonds were fixed round the end of a steel tube to form a kind of auger. This tube was rapidly revolved by compressed air and advanced so that its diamond points came into contact with the rock and water forced through the tube washed away grit and kept the tube cool."