In reply to SophieM89 :
Hi their.
In your production, can you please refer to the crop of rock as a crag and not a cliff? Cliffs are rock faces that the sea splashes against and where seagulls live, crags are inland rock formations that are normally the steeper part of a mountain or an "edge" of bedrock pushed up my a moving mass of land. It just narks me when a TV presenter refers to a mass of rock as a "cliff" and it isn't by the sea, shows that the producer hasn't done their research.
Central buttress on Scafell comes to mind, not quite sure it's the 150m (we're English, we use the metric system) you're looking for but it's about as steep as you're going to find in the UK, most of the steepest/overhanging stuff in the UK tends to be shorter. Closest you can probably get a road vehicle to the crag is Wasdale Head, from their it's about 1:30 to 2 hours hike (depending on how fit you are and how much gear you're carrying).
I'm not sure about the mountains you have their in London, but in the rest of the world, mountains don't have lifts.