It's Owen Greenwood's 'three wheeled' mini sidecar racer from the mid '60's. 1071cc Cooper engined, it raced in the unlimited class in the UK and was so successful at subverting the rule book that it was often made to start at the back of the grid! 
Excellent and correct answer. I saw this machine in action as a teenager, and loved the absurdity and audacity of it. The 'bike "establishment" didn't agree with my thinking, and saw it as a deliberate provocation. Quite why so few people copied the idea is beyond me, because, as you point out, it was way,way faster than the traditional sidecar outfits.
It was nothing new, really, since 3-wheeled Morgans had taken part in MCC events since post-WW1. I think that it actually had 2 rear wheels, very close together like the Isetta bubble-car, and because of their closeness they counted as one wheel, but I may be wrong.
(PS I hope the editors don't mind this puzzle, since strictly speaking it's a motorcycle - but in all reality it's a converted car. It retained the Mini front sub-frame, and had a tubular extension at the rear to carry the occupants and rear wheel(s)/suspension.)
