I'm afraid I'm more knowledgeable about Roman marble quarrying than about mining per se, so I can't provide good specifics about mines in Britain. I can however, speak a little to the shared characteristics of Roman mines and quarries.

Suetonius tells us that during the reign of Tiberius, "many states and individuals were deprived of immunities of long standing, of the right of working mines and collecting revenues." (Suet. Tib. 49). In the past this has been taken to mean that all mines were owned by the state. But more recent scholarship has qualified this so that now it is generally thought only some mines and quarries were owned by the state, probably those of the most import (gold mines in Spain) or those which required the most governmental involvement to operate (the porphyry mines of Eastern Egypt, which probably couldn't have operated at a profit without governmental support). Many quarries and mines remained in municipal or private hands.

There was a great variety in the administration of even those mines and quarries under governmental control. In general, such mines were under the control of a procurator metallorum, who may have been in charge of several different mines. For marble, there were imperial freedmen called rationarii who ensured that the emperor got the stone he needed quarried and delivered to Rome. Private purchasers worked with marmorii who specialized in delivering stone.

There were four principle ways in which the actual business of mining was carried out. First, soldiers could be used as miners. We know from Tacitus that an official by the name of Curtius Rufus used soldiers to mine silver in Spain (Tac. Ann. 11.20). Occasionally we find epigraphic evidence of a centurion who seems to have been in charge of a particular quarry. But it was probably more common for soldiers to tend to security and logistical concerns (making sure food and supplies arrived on time) than for them to do the actual mining. Second, slave labor could be employed, particularly that of criminals convicted ad metallum (to the mines). Third (and this was probably the most common option), the work could be given out to contractors, who would pay a fixed rate for the privilege of mining and/or turn over a proportion of what the produced. The contract specified where the contractor could mine but otherwise it was up to him to choose whether to bring in slaves or hire miners. Finally, the government could just hire miners directly. This was more risky than contracting out the work, and so tended to be the method used in places where it was difficult for contractors to operate at a profit (Egyptian porphyry mines are a good example).

As far as sources, you might have a look at A. Hirt's Imperial Mines and Quarries in the Roman World (2010). Its fairly dry, but may have more specific information about British mines.

Thanks to /u/Krazyhades (with a wonderful name) for summoning me: he/she is right to point in the direction of Cornwall, where indigenous mining had been going on for centuries before (after after) the arrival of the Romans. I suggest that you need to be considering the topic to be about Roman-era British mining, since this was not, as far as I know, carried out by Roman or other people from elsewhere in the Empire. Rather, the mining was a continued tradition executed by British miners. The Cornish were famous as miners for providing tin during the Bronze Age. Phoenician traders were reputed to have traded there, and whether or not that it was actually the case, it is clear that Cornish/British tin made it to the continent before the Romans made it to Britain.

You may want to look at one of several histories of Cornwall, written by Philip Payton, who remains the best historian of the peninsula.

You may want to expand the view of your question to include the non-Roman mining in England, as people there were skillfully extracting metals before the Roman arrival. Indeed, some Cornish miners kept to related work when they moved to the United States, being involved in mining far from their old world homes. I think I read some of this from /u/itsallfolklore posts regarding the folklore of miners?

In any case, I am not here to answer your question, but to express my hope that other people with knowledge of mining culture(s) in England will chime in.

What's a source/book for this topic?