Morris 1100 might be able to narrow it down for you (hopefully he will see this).
Otherwise do you know if many parts are original? Quite a few parts on a mini are date stamped e.g. wiper motor, starter motor, dizzy, coil, high beam switch, boot lock.
Check these things and it should give you an idea.
My car was sold new on the 10/2/67. It has a dizzy stamped '66, wiper motor stamped 7/66, coil stamped 8/66, starter stamped 9/66 etc The only thing that isn't original is the boot lock, but I KNOW that that has been changed in the past but it is stamed 4/65 I think
You should get the idea though.