This question is probably not completely answerable, but let's see how far we can get with some reasonable assumptions.
The object seems to have been made out of a brass cartridge case for an artillery shell. If it is "trench art", that implies it was done by hand, without power tools. That makes it unlikely that its diameter has changed much, and if it has, it will have got larger. Its length may well have been cut down. The puzzling thing is the rim around the bottom, which doesn't look like part of a cartridge case at all.
Which British WWI artillery pieces had cases of the right dimensions? Sadly, quite a few. We're looking at 75-78mm calibre and a case length of 110mm or more. We can eliminate weapons designated as "BL", because they did not use brass cartridge cases, but loaded their propellant in cloth bags. So we can limit ourselves to the other type ,"QF" for "Quick Firing" guns.
The most common British gun in WWI was the QF 18-pounder gun. That took an 84x295mm case, which seems unlikely to be the parent of this item, since its diameter is too large, as are those of many other large guns.
The QF 12-pounder 8 cwtgun and QF 12-pounder 18 cwt naval gun are unlikely, as primarily naval weapons.
The QF 13-pounder gun is a possibility, as are the QF 15-pounder gun, QF 2.95-inch mountain gun, 75mm AA gun, QF 12-pounder 12 cwt AA gun, QF 13-pounder Mk IV AA gun (very rare), QF 13-pounder 9 cwt, and the QF 3-inch 20 cwt.
Without more clues, or help from an artillery cartridge collector, we're unlikely to get much further.