Personally I don't think there will be a DD-E number for the Thompson chest simply because the Thompson guns were imported direct to Ordnance via the inspection branch at Woolwich then to Ordnance at Weedon (or where ever but likely, Weedon. Borne out by the photos of them being unpacked/packed by Ordnance Corps there). Therefore any shipping/transit/issue chests will have been drawn-up locally and contracted for in-house. Just my view as how the system works.

Same as many things from Ordnance, such as tank tracks to my knowledge......... Special pallet made by Ordnance contract and returned with old tracks. As a matter of interest in Thompson things, the little steel boxes with a steel fold-over handle that hold 6(?) 20 round Thompson magazines. These boxes were originally used as a secure container for spare valves for the old tank radio sets and kept in the tanks or radio repair trucks (usually the old Commer 5 ton lorries called Commer Binners). The little inserts were added to accommodate the rear of the magazines. Just a useless bit of Thompson info. We used to use these boxes for all sorts of things