I Britain anyone finding a historic treasure is required by law to report the find to local authorities.
The find is then turned over to a local Archaeologist to excavate.
The finder is then given a monetary reward % as defined by law based on the appraised value of the find.
The finder does not get any of the actual treasure.
You are correct about the UK law, however, not all metal detectorists follow it. They dig it up and put it on eBay or other similiar site. If they do report it, they do split the money with the land owner. If a museum or other institution does not buy it at the appraised price, then the artifacts go to the finder and land owner.