Mineral rights in that part of the country are mostly owned by the Duchy. When the mines were at work it was under licence and percentage of a mines ore sales had to be paid to the mineral owner as 'dues'. There are exceptions, Trevellas Coombe mineral rights are owned by Colin Wills if he is still around, hopefully. This is the Blue Hills stamps were you can visit for a small fee.
Tom is a director of Natural Amenities Ltd which owns the Craig y Dinas mineral estate. Soil landowner is Welsh Government. This situation of separate ownership was caused by what is called a "severance" wherby land gets sold but the vendor retains certain rights. This can be Minerals, Mines and Minerals (Dinas), or other rights such as Sporting. Its a complicated business and there are also Manorial Rights and other kinds such as in Royal Forest of Dean. Separate mineral ownership, as legendrider touches on, can cause issues, and awarness arose in 2010 with Countess of Lonsdale V Tesco
Compensation for what has become known as "mineral trespass" is small, but the power lies in the mineral owners ability to raise a stop notice and then go for an out of court settlement, usually known as "Ransom Money"