Your date for the introduction of handheld gunpowder weapons to England is wrong. It was the 1320s when gunpowder weapons became widely known. In 1326, King Edward III was presented with De Nobilitatibus, sapientii et prudentiis regum, a book of advice that contained a section on gunpowder warfare. It was produced in London, along with a companion manuscript called De secretis secretorum Aristotelis which was in circulation by the end of the year. However, the first clear use of gunpowder as a weapon by the English was not until the 1340s and from 1326 to 1343 the only clear reference to gunpowder at all in royal records is an entry in the accounts of John de Flete from 1333-4, a crown official who used Exchequer funds that year to buy very small quantities of gunpowder ingredients. Guns weren't mainstream, but there was some limited interest in experimenting with gunpowder in England in the early 14th century.

The French, on the other hand, were keen adopters of the new technology and introduced it to the Hundred Years War almost as soon as they could get their hands on it. In 1338, at least one French ship was armed with pot-de-fer, a primitive vase shaped cannon. In 1339 Edward III’s attempted to attack Cambrai, and the English army came face to face with French ribault, a cart with a load of guns set off at once, and it scared the crap out of them. Although early gunpowder weapons were generally ineffective at actually killing people, they were terrifying. These days, we expect explosions in war and we're desensitised to it. To them it was all new. The French regularly used gunpowder and the English needed to respond. England did have ordnance at this time, but it appears that very little of it came from sources for which we have records; that is to say they were not produced for the crown or purchased by it. The first account of any guns in English possession is ‘engines with powder [and] wildfire’ during the Siege of Tournai in 1341. The first clear reference in any crown records to ordnance is to repair weapons, not to create or purchase new ones, on the order of Edward III on 1 February 1345. It is therefore likely that England’s first guns were refurbished and redeployed weapons captured from the French. On 1 October 1345, the first newly crafted firearms were produced for the English crown, as the king ordered the production of 100 ribaults, representing a substantial increase in the gunpowder weaponry available to the English. It seems that Edward III realised the extent to which England was lagging behind its neighbours with regard to the adoption of technology and was very keen to correct the situation and join the French crown and cities in the Low Countries in pioneering the new technology.

Only five of those 100 guns would actually be ready for Edward’s raid through Normandy, but they proved their worth at the Battle of Crecy. Despite their limited deployment, they left an impression. Giovanni Villani, part of the Genoese contingent of the French army, wrote that:

"The English guns cast iron balls by means of fire...They made a noise like thunder and caused much loss in men and horses... The Genoese were continually hit by the archers and the gunners... [by the end of the battle], the whole plain was covered by men struck down by arrows and cannon balls."

Whilst Villani is obviously being dramatic, his experience makes it clear that the English use of gunpowder was really getting somewhere. In the Siege of Calais in 1346, the English used 20 gunpowder weapons to block the entrance to the harbour including bombards, which fired large stones rather than the barrage of small lead shot which characterised the ribault. By 1350, small numbers of gunpowder weapons were a common sight on the battlefields of Europe, but especially in the armies of France, Burgundy, Brittany, and England, who all looked to new technologies and tactics to gain an advantage in the war. With a surge in demand from the royal army, the private armies of the nobility also looked to improve themselves by purchasing gunpowder weapons. Financial records tell us that the Founder's Guild in London (which also made stuff like bells) was producing hundreds (and perhaps well over 1000) of these things a year, along with the lead shot and gunpowder bags to go with them, and it's unlikely that the crown was their only customer. By the 1380s a gunpowder weapon could be bought for around £1 (easily affordable for the gentry), and could be purchased from guilds in many English towns.

So what were these guns? The common term for them was "handgonne", or something close to that depending on regional spelling. The 14th century ones were generally a tube, usually made from cast iron but sometimes from copper, mounted on a stick that was couched beneath the arm like a lance, or balanced on the shoulder. Here's a depiction from a 15th century manuscript. And another, from a 15th century Flemish manuscript.

The user would pour gunpowder into the barrel, followed by their shot, they'd pack it all down, light the fuse, couch the weapon (or maybe balance it over their shoulder if they wanted to aim more precisely) and point it at the enemy. At close range, if you got hit by one of these things, you were dead.

By 1389, handgonnes were certainly advanced technology, but not hard to acquire or use.

Sources:

McLachlan, Sean. Medieval Handgonnes: The First Black Powder Infantry Weapons. Bloomsbury Publishing, 2011.

Spencer, Dan, ‘The Tower of London and Firearms in the Reign of Edward IV’, Arms & Armour, 13 (2016), 98–110

Tout, T. F., ‘Firearms in England in the Fourteenth Century’, The English Historical Review, 26 (1911), 666–702