I think you have a hybrid of a 2pdr No.2 armour-piercing projectile and a 2pdr 'pom-pom' AA gun cartridge case. You can see a picture of both types here:
http://www.bocn.co.uk/vbforum/attachments/AAAA2pdr.jpg
Tank gun
Ordnance QF 2-pounder - Wikipedia, the free encyclopedia
Naval gun
QF 2-pounder naval gun - Wikipedia, the free encyclopedia