Great question Peregrine and it's going to get the grey matter stirring for the Bren fiends out there BUT.......... so far as the REME technical data and parts lists are concerned, there are 3 types
The Mk1 is the original, full length of 21 3/4" long measured from the butt seating to the front. The identifying feature is the small protrusion at the front left hand end that was to act as a bar to incorrect assembly of the gun
However, the wise and more knowledgeable will now hopefully come in and mention the post August 1940 simplifications that took place. For example, I believe the rear scaloped machining close to the butt socket area was also simplified..................
The Mk2 is SIMILAR to the Mk1 in profile but the front end is cut short by 1.5" or so and ends just in front of the mounting pin hole. Also, the pistol grip is now secured by a standard BSF bolt instead of the Mk1 type hollowed (?) grip screw (that was initially designed to hold an oil bottle)
Once again, hopefully, some of the more knowledgeable will be able to come in and identify the variations and hopefully, identify the Candian versions
The Mk3 butt slide followed the Mk1 pistol grip style, with hollowed pistol grip format but the shortness of the Mk2 type and the vertical side frames reduced in depth by about 3/8" or so.
Confused yet...............?
The Mk4 was a Mk2, lightened/converted to Mk3 lightweight spec. These were not adopted in any numbers but they have turned up occasionally. I understand that some of the ex Indian Army Brens that are available have these 'Mk4' butt slides fitted. While the Mk4 Bren didn't feature in our order of battle, they did feature in the Indian Ordnance parts lists as Mk4 guns.
Phew.......... Those are the basic variants Peregrine that you probably knew/understood. Can you shed and more light on this interesting subject KG, Brit P and ZGB among others