The first documentary evidence of gunpowder and artillery in Europe dates to 1326, but it was only around 1350 that gunpowder becomes more frequently referenced. Artillery seems to have been utilized by the English at Crecy in 1346, but clearly had been introduced to England far earlier (a manuscript indicates that artillery was at least known to Edward III in 1327). Royal English accounts indicate that by 1383, the king's armory was in possession of at least 53 guns of various sizes, with the majority weighing in at approximately 380 lbs. Guns became more and more frequent (as well as larger in size) after 1375, and by 1410, they are fairly common in arsenals and considered to be extremely important in sieges, although they had not yet entirely replaced trebuchets and mangonels.

So yes, guns were present in Britain starting in the 14th century, although their impact seems to have been somewhat marginal until the very end of the century. From the 15th century onwards, artillery becomes exponentially more important and useful in both sieges and in pitched battle.

Source: Robert D. Smith, "Artillery and the Hundred Years War: Myths and Interpretations," Arms, Armies, and Fortifications in the Hundred Years War.