Just spoke to a friend who was down at lulworth this evening, security saying they don't want people climbing there (Stair Hole) at the minute until things calm down a bit after all the upset at Durdle Door over the weekend. (Couple of weeks apparently suggested but obviously depends what happens next weekend?)
Whilst technically it's access land (there's a climbers code of conduct linked on the rad here https://www.thebmc.co.uk/modules/rad/view.aspx?id=161 - the part about not encouraging the public onto the cliffs obviously very pertinent at the moment) it's probably best not to right now, no value in antagonising people.
Just to flag the rad has now been updated, key paragraph below:
COVID-19 Update: please avoid Stair Hole for the time being. The recent spate of tombstoning and associated accidents at Durdle Door has caused serious concerns to the landowner. Whilst DWS and climbing are clearly very different, from a non-climbers perspecitve they are no different. As a result, for now please avoid Stair Hole for climbing whilst attention is focused on the area to prevent future access issues. This page will be updated once the situation changes.