A 10 metre high sandstone bluff rising out of the Hart Burn at, wait for it, Hartburn. There are few reasonable looking lines. The river is usually very shallow at this point so, although the possible lines start in the burn, a large stone would suffice to keep the feet dry. Gardening would, obviously, be out of the question here, so it isn't worth the effort of getting permission(unlikely) and getting your feet wet for a vegetated route whic no-one will ever repeat.
Unnamed Sandstone Carboniferous Namurian (Upper Limestone Group)
Loose looking and vegetated.
The wood is managed by the Woodland Trust who permit public access, but who would be unlikely to be too keen climbing on the crag since their remit is to encourage wildlife, especially trees and plants, some of which grow on crags.
No recorded problems.
Other interesting stuff:
The strange grotto is Hartburn Glebe. This was constructed in Victorian times by the Vicar of Hartburn Parish as a sort of summer house for the ladies to bathe in the river from. A tunnel can be seen going under the path built, allegedly, so the ladies could enter the water discreetly.
If you follow the path around the top of the woodland the line of the Roman road, the Devils Causeway can be clearly seen as a hollow trackway slanting down to the river where the remains of a bridge abutment lie in the bank. In the river bed is a series of holes, some of which still have pieces of wood in them, and which probably carried a bridge across.