This is the BMC Mini-based Zagato Mini Cat, made in glassfibre and based on the floorpan of the Minivan.
It was shown at the Earl's Court Motor Show, London in October 1961.
Inevitably Zagato were hoping for a production run but equally inevitably only the one was ever built...
Zagato did, however, use the basic design (but with a different front-end) for their Hillman Imp-based Zimp a couple of years later.