Uh-Mazing. Love hearing about this stuff. ...Nope, still in no hurry to go looking for class rings in the local park....
There must be a dozen or more people here who know lots more about this, but my impression is that that's only true initially, so that the finds can be recorded. If they're on a level vaguely corresponding to 'national treasure,' the finders are compensated. If not, they can keep the coins themselves.
It does have to be reported - to the Portable Antiquities Scheme, which on the surface sounds a bit heavy handed - but finders are duly compensated if the PAS determines that a museum should benefit from a historically significant find. Otherwise the PAS returns the item to the finder. Here is a token I own that was found by a detectorist in rural Shropshire in 2007: After he reported the find, it was cataloged and returned. It is a fairly common Irish token from 1672 - but unusual because it turned up in rural northern England demonstrating a possible trade route etc. When I purchased the token from the finder he had to secure an export license from the PAS to send the coin out of Britain - a fee free service that took about 3-4 days and then he shipped the coin to me. So this coin has documentation of where and when it was found and the significance of it's being found. It adds an uncommon provenance to a rather common token. So far from being heavy handed authorities - the PAS is actually beneficial to the crown and collectors and detectorists.
Excellent points, both about how benign the process is, and the A1 provenance that collectors end up with, as a (Huge) fringe benefit.