British whatsit?

[RT Ellis]

It's difficult to get a sense of the size of the item from the images. It's possibly a carrying case for the Thompson SMG, at least it is similar to the carrying case known to have been for the SMG M1928, illustrated in the U.S. Army Ordnance official image attached:
Attachment 52364

The pouches assembled to the your carrier are certainly dissimilar and appear to be intended to contain bulky components, that suggests a carrying case for communication equipment.