That appears to be a cartridge case for the QF 3-inch 20 cwt anti-aircraft gun. The "3in 20 cwt" marking on the base clearly indicates that.
That nomenclature means the gun fires 3-inch diameter projectiles, and the barrel and breech have a total weight of 20 hundredweight, or one long ton. That was a Royal Navy convention for gun designations, which I think originated in the nineteenth century and survived into the twentieth; larger guns were weighed in whole tons rather than hundredweight.
The gun was hastily introduced in 1914, when it was realised there were no suitable weapons for defence against German airships and bombers. It was designed and manufactured by Vickers. The design seems to have been based on the QF 12-pounder 18 cwt naval gun, with modifications to a War Office specification. It was used on ships and the Western Front, and stayed in use for second-line roles until 1947.