Fixed it for you.
The government doesn’t get any money. All it means is that they have to give museums the opportunity to buy them first. Both landowner and discoverer get to split the value of the coins whether the museum buys them or not.
I finally researched this; here is the answer:
“Will I have to pay tax on valuable finds?
If you sell a valuable find, you will be liable to pay capital gains tax (CGT) on any amount above the annual exemption of £10,100 per person.
Stephen Herring, a tax partner at BDO Stoy Hayward, the accountancy firm, said: “It would be very unlikely that HM Revenue & Customs would view a casual discovery as a ‘trade’, so it would not apply an income tax treatment. They would probably anticipate that more people would make a loss in any case. Accordingly, a disposal would be treated as a capital gain. Above the £10,100 annual exemption a fixed rate of 18pc is payable.”
An additional “chattels exemption” would probably apply, he added. “This applies, on an item-by-item basis, where the proceeds of the sale of tangible movable property, excluding currency of any description, are under £6,000.”
British gold sovereigns, which are still legal tender, are exempt from capital gains tax, Mr Herring added.”
So it doesn’t seem like the tax would be as great as the tax on ordinary income, and it would not be subject to National Insurance Tax like ordinary earned income.