If I recall correctly, the longbow wasn't even very popular in the English army until Edward I (of Braveheart fame) encountered their deadly capabilities at the hands of the Welsh during his campaigns. (1276-1277 & 1282-1283)

The longbow was extremely effective in Welsh warfare, which relied a lot more on hit and run tactics, and ambushes compared to the heavy cavalry based combat of the English and French.

Out of lazyness, I have cited wikipedia:
http://en.wikipedia.org/wiki/Welsh_longbow#History