For sure there was at least one recorded four wheel drive Mini built; the one that John Cooper nearly killed himself in during the springtime of 1963, In fairness to accuracy it is highly likely that BMC had precious little to do with this car's existence. It was almost certainly the work of the Cooper Garage. However the close working relationship of Charles and John Cooper with the management of BMC makes it quite possible that BMC knew of and was following this car's development.
It is also reasonably well recorded that there were several, (in the order of 10 or so), 4WD Mokes built in the UK and Oz as factory prototypes built to encourage military interest in the Moke, (without much succees of raising interest).
As far as rear wheel drive Mini's go it is very unlikely that even one was ever developed even for prototype purposes by the BMC factory or at least as my fading memory allows to be remembered. ;-(
As many low volume constructors demonstrated it is/was an easy job to place the entire front wheel drive assembly in the back of very functional sports/racing cars. Australian builders Lolita and Nota as well as UK's Marcos come prominently to mind. The Nota Fang with 117 recorded as being built with BMC power is likley the most prolific.
Edited by Joe Bosworth, 29 August 2014 - 12:39.