the spindle of which would contact the primer, it seems likely that it is intended to check primer seating depth. It is my understanding that Britishmilitary ammunition which was loaded with Cordite was necked after the charge was inserted, so that it would have been primed while still un-necked, and the pictured tool seems suited to such a condition.
Alternatively, if the micrometer spindle nose is wider than the primer (can't tell from the photo, though the fact that it is tapered rather than straight makes this less likely), the device may be intended to check the thickness of the case head web.
mhb - MIke