This sort of question is more interesting when we don't narrow it down to one country but have one answer per country. In that spirit, this answer is for:
There are a number of airfields with very short runways, probably one of the shortest licensed runways is Netherthorpe at 382m (LDA 308m)
Unlicensed you'll have a few to pick from. Grass runway at Gloucestershire Airport is 305m
Often quoted as challenging is Barra which is the only airfield situated on a public beach.
It's unclear whether this airfield is still open, it's not shown on any guides, but one of the most challenging airfields must be Vallance-By-Ways. It is situated a couple of hundred meters from Gatwick Airport's runway. You can watch a (pretty scary) video of someone landing a microlight there.