I'm not a historian, but this doesn't match my understanding; that true weapons like swords and crossbows tended to be restricted, and peasants used scythes, clubs, etc. instead.
Arround 1400, the King proclaimed that "every Englishman or Irishman dwelling in England must have a bow of his own height", at one point Tennis was banned to give more time to bow practice. By 1500s every man had to buy his 7 year old son a bow and teach him how to use it, and a bow+arrows must be kept in everyones house.
Crossbows on the other hand were practically banned, but this was more because a highly skilled longbowman was more deadly