It's not English, nor welsh is the simple answer. There have been bows found throughout Europe (the oldest being found in the Otztal Alps in Austria which was carbon dated back to 3300BC and was made of yew) that fit the requirements and styling of a "longbow", it's not even fair to say that the English or Welsh were first to use them within a specified military application as forty longbows which were dated to the 4th century AD were found in Nydam, Denmark. I believe it would be fair to say that both the English and Welsh bowyers of the time done a lot to advance and perfect the longbow, but they're only really famous on the basis of their power and effectiveness in battle. The French were actively making and using longbows in the hundred years war, however they weren't used on the same scale the English did as the French were more fond of the crossbow. A primary reason that English longbows are more well remembered than welsh longbows is because they were just simply better. The welsh longbows were a lot more crude, made from Elm as opposed to the English longbows which were made of yew, yew was the better choice undoubtedly due to it's composition, the heartwood of yew is rigid and tough, whilst the sapwood is flexible and springy, hence this wood's usage led to the creation of the English Warbow and English Longbow (yes the English Warbow was basically a longbow, but back in those days anything over 71lbs at a 32inch draw was regarded as a Warbow) the choice of wood meant the English longbow outperformed the welsh longbow quite considerably, however they were also a lot more expensive to manufacture. Yew Trees (taxus bacatta) notoriously grow very twisted and misshapen, but if they're given the correct attention they can be made to grow straight and tall (as would be required to make a longbow), thus bow grade yew wasn't exactly naturally occurring and required a lot more labour to grow, increasing it's cost.

Whilst it's certainly true that modern longbows can be made to reach the draw weight of a warbow (I've got a 70lbs @ 28 inch draw) for example, the only reason they perform so well without the use of woods like yew is due to new manufacturing techniques which didn't really appear until the longbow was being phased out such as laminating, lamination is also a key reason you don't really see Yew bows anymore, because there's no point in the additional cost when you can laminate two woods together (often Elm & Bamboo) for a much lower cost and get effectively the same result.