In many medieval RTS games soldiers come out of a building named 'Barracks'. Where did medieval soldiers actually train ? Did such specialised buildings exist ? Most peasants probably got no training at all, and nobles trained at home I suppose, but what about levy troops that did train ?
The use of mercenaries by the English is not surprising, since the old "feudal" system of raising armies (a system that had never really worked on a large scale) had been pretty much abandoned in Europe.
As such, knights and the like did have specialized training areas (as under livery and maintenance), but the bulk of armies was composed of mercenaries and the self-trained. This is, incidentally, why the English longbow and quarterstaff took off; the bow was already used by peasants to hunt, and the quarterstaff was popular among the peasantry for self-defense.