@Foofie,
Simple answer: the queen.
Complicated answer: the finder must report the find to government authorities within fourteen days, pursuant to the
Treasure Act of 1996. The government then may give the finder (along with the owner of the land) a reward for finding the treasure.
One question that I'm not able to answer is whether the Treasure Act applies to the Channel Islands, where this particular trove was found. The Channel Islands occupy a rather strange jurisdictional place in the UK. They're feudal domains ruled directly by the British monarchs in their capacity as dukes of Normandy. Legislation that covers England, Wales, and Northern Ireland, therefore, may not necessarily cover the Channel Islands.