There was an article in Classic Arms Magazine in 1999 on loading the 310 Cadet Rifle, I used this as the basis for my reloading and shoot out to 300M quite accurately.

Modified 32/20 cases thin rimmed.
North Devon Fireams Services (NDFS) Dies
RCBS mould designed & sold by NDFS
4.5grns of unique
Lubed with Lees Liquid Alox

Jim at North Devon Firearms told me that he found Military 310 cadet rifles would often accept the 32/20 cartridge case without being thinned down, but this was not generally the norm for commercial rifles in 310 calibre, sadly NDFS are no more.