According to the Treasure Act in Britain, anyone who believes they have found a metal object more than 300 years old is required to report it to the authorities within two weeks. A judgment is then made on whether the discovery meets the definition of “treasure.” Later, a valuation would be given, rewards may be offered and museums have the chance to claim the objects.

Instead of following the rules, Mr. Powell and Mr. Davies kept quiet and soon began selling the valuable coins to private collectors.

The hoard, a mix of ninth- and 10th-century objects, included Anglo-Saxon coins, a gold ring and gold band, silver bars, and a crystal rock pendant, according to a police statement.

Photographs of the artifacts in a freshly dug hole were found deleted on Mr. Davies’s phone by the authorities.

Despite a yearslong investigation, only 30 of the 300 coins the men are thought to have found have been recovered, in addition to some pieces of jewelry and a silver ingot.

The rest of the treasures are missing, presumed hidden or sold, according to West Mercia Police, the force that covers much of western England.