In the UK, by law, found treasures must be reported. The treasure is examined and valued and museums may bid to buy it. Once sold to a museum or public institution, the prize money is divided among the finders and the land owner.
This system works very like the old Admiralty courts who handled prizes seized by the Royal Navy and privateers. Prizes were the property of the Crown, but these courts rewarded those who had taken the risks. If the prize had been illegally seized, the Crown kept the whole thing.
Found buried stuff is called treasure trove. It, by law, belongs to the Crown. The coroner determines if it was lost (finders keepers) or hidden (treasure trove). If it is treasure trove, the government will sell any part of it that interests museums and turn the proceeds to the finders/landowners. That which doesn’t interest museums is returned to the finders/landowners to sell on their own.
From what I’ve heard/read the government plays fair in the business of treasure trove to encourage such finds be reported. This allows pros to do the recovery and examination of the site. Otherwise, important information is lost forever.
The guys broke the law. Don’t know if they deserved the amount of time they got, but messing with the Queen’s property is a big no no. I’ll bet the penalty for killing swans is pretty harsh.