Lesjcbs, I don't get it. If you or I find something on "farmer bob's farm" here in the USA (with his permission) worth $1,000,000, then guess what? That's entirely between you and farmer Bob as to the split, or who gets it, etc.... The government here has no say-so about those gold bars on farmer bob's land, since ..... doh ... it was FARMER BOB'S land. I don't need the USA's "thankyou". Nor do I need the USA to buy it from me at what they consider the "fair market value" or to "grant me that I can keep it". It was and is simply mine (or farmer Bob's) to begin with. We can put it on ebay and let the fair-market value prevail. So how, oh how, oh how, is the British system superior??
As for the things found on public/federal lands, as I told you before above: The UK guys who are getting those thankyou's and buy-outs are not finding them on british federal lands, if I'm not mistaken. And CERTAINLY not on sensitive archaeological sites there. Hence the UK system is not a positive incentive to go finding things on federal land there, since I think (correct me if I'm wrong) their federal lands are not free to tromp on with md'rs, the same as the USA federal lands have supposed limitations as well. That's why you rarely hear of British hunters doing park turf, or public forests, etc... (correct me if I'm wrong). They almost exclusively do farmer's fields with permission.
Hence neither the british, or the USA system rewards or encourages or incentivizes the hunting of federal lands. In other words, in the same way we have limitations here on federal lands (and/or especially sensitive archie historic monuments and such), SO TOO do the British have their laws for places not to detect. And their "rewards" system of buying people's stuff and thanking them, does NOT allow them to hunt "anywhere nilly willy".