Maybe "sort of" the same size as the .450/.400........as in generic calibre?
If one is speaking of the classic .400 Purdey the 3" straight case is closely similar in base and rim size to the 9.3x74R. The original ammo called for a .404'-.405" 230 grain bullet.

Maybe that classic bullet diameter of .404-.405" calling for special barrels bore/groove gave Purdey indigestion? Cannot be lack of available ammunition because modern Kynoch does list the Purdey .400 3" tho no idea what bullet diameter they use.
- Mike

EDIT: I looked at the Woodleigh list and sure enough they offer a proper .405” 230 grain bullet.