I've had a look through various Australian Mini parts books and engineering drawings. The following is what is documented by BMC, so not necessarily what occurred in practice, although I've no reason to think differently. Only the Mini saloon jack is discussed here. Mini van jacks are of a different design.
The jack specified for the Mini saloon from November 1965 through to final Mini production in Australia (end 1978) is part AYA2156 (example pictured below from my MK II S). The engineering drawing shows it to be 18.44 inches high from the base to the top of the screw nut. The finish is black lacquer. It has an instruction decal with white writing and diagram on black background affixed to the flat of the upright. The jack was made for BMC Australia by APAC Industries (Finsbury, S.A.), later to become Clyde-APAC.
The previous version of this jack, part AYA2054, is shorter at 15.25 inches high and was released into production in March 1964. Prior to this date I believe UK manufactured jacks of the same basic design were used but I'll do a bit more investigation on this.
Apart from being 3 inches shorter, the earlier jack (AYA2054) is missing the short piece of 1/2" bar welded to the lifting lug (see drawing below). I assume this design change was to limit the travel of the lifting lug, for safety or metal fatigue and stress reasons. Also, in September 1964 the background to the instruction decal was changed from transparent to black. No idea why, although I've heard transparent sticky labels are difficult to print on, so maybe the instructions were being rubbed off over time.
I believe the jack handle with hub cap removal tool on the end was always red in Australia.
Attachment:
AYA2156 Mini Jack 1.jpg
Attachment:
AYA2156 Mini Jack 2.jpg
Attachment:
AYA2156 Mini Jack 3.jpg
