As opposed to the principle of "Govermentus Takus?" Which governs in England?
I know it's a joke, but the answer is actually somewhat interesting. Because of the amount of potential archaeological discoveries that can be made in a country like England, the laws actually consider these issues in detail.
In this case, the owner of the property would have the right to the found material, as it does not fit the legal definition of 'treasure'.
If a found object is found to be treasure (in essence, to be treasure it needs to be at least 300 years old and substantially made of gold or silver, or prehistoric and substantially made of any metal) a person is required to offer it for sale to a museum at a value set by a government committee - they get to keep that money if it sells. If it doesn't sell, they can keep the object. The government cannot just take it (although with an object of major historical importance, the British Museum or some similar body would probably be the buyer after the committee set the price).