Bad air (of various sorts and due to various causes) is very rare indeed in UK non ferrous metal mines. If you are visiting mines that are in guidebooks (such as Derbyshire caving guides) then the rare instances where such dangers might exist will be clearly mentioned in the guidebooks.
Problems are largely confined to coal mines and to stratified ironstone mines; neither class of mine sis widely visited by mine explorers and the limited number of people who are active in those fields are mostly well equipped with gas detection equipment.
In reply to your mention of things to take: boilersuit, wellies or boots, soft-soled wetsocks (you'll often encounter water deeper than wellies), helmet with light mounted on it (you'll need your hands free for small climbs and scrambles at times so a hand torch tends to be an encumbrance), small rucksack with food, drink and spare lighting - those are the essentials.
A camera might be worth taking but it'll need protection from damp, mud and knocks and bumps.
Some people take pencil and paper to make notes of routes and where they've been - never paint arrows or anything on the walls; if you are uncertain about route finding, sketch a plan of complex areas as you go. You will rarely see good minerals in well-trodden mines so don't bother taking a hammer - mineral collecting is not universally well-regarded anyway (many fine exposures have been ruined by indiscriminate hammering). The old saying "take nothing but photos; leave nothing but footprints" is a fine guide to how to behave - no one likes seeing litter or paint in historic mines or in natural caves, and artefacts and minerals are best left in place for others coming after you to also see and enjoy.
In your vehicle it's wise to have a complete change of clothes, a towel, and sacks or carry crates for your mucky gear. Oh - and money for the inevitable trip to the pub afterwards!