Fish was well-watched by the nobility. You took a fish from a river without getting permission and you were a dead man. In fact, game was controlled as well. I know that Richard the Third was anxious to reform some of the overly-restrictive laws about salmon fishing and may have done so.
The king wouldn’t have enough men to patrol all the rivers and forests, especially the outer reaches of his land. Much the same as the day of US slavery, you don’t want your workers dying of starvation or ill treatment.