A good point: someone needs to hunt through the statute books for these. In many cases (I'll guess) you will find that the situation is something like the following.
This is a summary of http://web.raex.com/~agincort/arch-laws.htm, which credits one Nigel FitzMaurice* for tracking it all down.
The laws making archery practice compulsory were instituted because people spent too much time gaming and drinking (it's hard to imagine what it must have been like in those days, isn't it?), so the same laws also regulated betting, ale-houses, and so on. In the third year of Henry VIII (1511) ownership and use of bows was made compulsory for most men under the age of forty. This law was made perpetual in 6 Henry VIII (1514) and confirmed or rephrased in a law of 33 Henry VIII (1541).
In the 1541 law all men and man-children between seven to sixty are required to have a bow and arrows. The law also forbids foreigners from taking bows overseas, regulates where bowyers and fletchers may dwell and what they may do, and so on. Other sections of the same chapter regulate bowling, dice, etc, etc.
The 1511 law was repealed in the 1863 Statute Law Revision Act, whose purpose was to clean out an enormous amount of the dead wood of mediaeval law. And the applicable chapter of the 1541 act was repealed in 1960 under the Betting and Gaming Act.
* Hey! Nigel FitzMaurice is at least a real person, and an old friend of our own kmcardle. Small world.