I picked up this back in the mid seventies in a mixed lot from Kynoch of components. There was a similar, but different dimensioned case that another collector had.
It is an unfinished case, formed but not headed so there is no primer pocket, headstamp or extractor groove. Length is 3.153" (80.09mm), head diameter is .641" (16.28mm), shoulder diameter .596" (15.13mm) and neck is .281" (7.15mm) external, .241" (6.1mm) internal.
I am inclined to think it may have something to do with the Broadway Trust Corporation recoilless project but the calibre is wrong, as the BTC round was 7mm (or at least the small calibre one was).
.303 gives comparative size.