I can't offer anything definite, but a British order of '36 included three 2pdr AT guns at battalion level too (despite there being insufficient of them to equip the majority of infantry battalions in that year). As it was in development prior to being accepted in October '35, perhaps the UDF '34 order more or less 'pencilled it in' (as part of the 'five year plan'?).
That being said the British bought 12 French 25mm AT guns in '35 for the Middle East command and had bought a similar number of 20mm SEMAG-Becker dual-purpose guns in the late '20s. It was later to buy some 37mm Bofors AT guns in '38 (iirc). Any of these 'might' have been in mind for the ACF when the instruction was issued... my money is on the 2pdr though.
I managed to find reference to 500 Bren Guns being ordered in '35 and the comment that only 15 had arrived by '37, here:
https://www.academia.edu/2538332/The_Union_Defence_Force_Between_the_two_World_Wars_1919-1940 The '13-man section' sounds very much like that of the British from WWI, in which case only two of the four sections in each platoon would have a Lewis Gun. These were led by a single NCO (2 with LMGs by Sergeants and the other 2 by Corporals). Platoon HQ was just a Platoon Leader accompanied by his Batman and a Platoon Sergeant. Reductions in manpower in the '30s led to the British dropping these sections to just 8 men by '36 and two of the four platoons in a company being commanded by a 'Platoon Warrant Officer' (with no Batman). Ultimately this evolved into the three-sections of 8 men per platoon, but with each section having an LMG, organisation of '39.
http://www.warestablishments.net/Great%20Britain/Infantry/Infantry%20(Mixed)%20Battalion%20July%201936.pdfI know the UDF re-structured in '34-'35, but whether they stuck to the 'old' organisation, or the 'new' British one you'd have to judge for yourself. The British decision was bought about by lack of recruits and cash; I suspect the UDF's concerns may have been more pragmatic given their perceived role in Africa and they may have stuck with the bigger sections to absorb attrition via the various perils of Africa. This may of course have ended with them only having the same number of men as the equivalent British unit had active service been required.
How these were deployed I don't quite know. At some point before '39 there was a change to the gun group and a manoeuvre (rifle) group in each section we are used to. Prior to that though it was a two section gun group led by the Platoon Sergeant and a two-section manoeuvre group led by the platoon commander. There does not seem to be any sub-section breakdown in this organisation pattern.