Hmm, I was just about to jump in with both feet and nominate the Snaefell mountain railway in the Isle of Man, but fortunately I checked first. (
wonkypedia link here..
Snaefell mountain railway.)
I knew it had a centre rail, and having never ridden on it just assumed it was rack & pinion.
According to web sources, the centre rail is for emergency braking but not for traction.
Well at least I saved myself a public drubbing. Phew !
BW.
Edit: I've just been informed by SWMBO that the IOM isn't part of the UK, so it wouldn't have counted anyway. Oh dear.