Although there ironstone workings in the immediate area and this looks like a drift I dont think it is.
I think this is more likely the location where the culvert from the Boulby Alum Works passed underneath the road on its way to the Alum House for processing.
The house is probably not original, although a wall in the garden at the edge of the cliff looks much older. The vertical shaft from the Boulby Alum Tunnel on the shore would emerge in the garden of this house were it still open.
Aislaby Quarry was a source of blockstones in the 17th and 18th Century for harbours such as Whitby, Margate and Ramsgate, and the Strand Bridge in London.
The blockstone was returned from the Whitby pier in 1964
The quarry reopened in 2002, I have read that in the 1970s the remains of a jet mines were also accessible, but the whole area seems to have been freshly opened up, so I doubt the current owners would take kindly to visitors searching for any remains.