Reading that article makes me wonder. I had a kidney removed due to cancer in 2001, and a minor basal cell carcinoma on the face removed this year. The article says that both can be due to radon.
But most of my time underground has been in Scotland, with some at Dyliffe, and maybe a few minutes here and there in some Cornish adits, including one on Kit Hill and some on the coast. I don't imagine the radon level is significant in Craigend limestone mine, for example, but it may possibly be along the Ochil Fault (Blairlogie, Carnaughton Glen, Silver Glen etc) and possibly at Leadhills/Wanlockhead where I have spent considerable time in the late 1960s in some workings which are now inaccessible.
I guess we need to be careful, and it would be useful if people with suitable equipment did check out as many mines as possible. In particular, anyone going to Tyndrum/Cononish would be well advised to check for radon, as there is definitely uranium in the area.
But as we saw the other day in Edinburgh, gas is a more immediate hazard in many cases. I never go near old coal mines for that reason, even though I know where there are some still accessible.