The igneous rock (whether extruded as volcanic rocks or intruded as a granite or similar rock) doesn't contain any significant amount of radon; what matters is the concentration of uranium (and some other radioactive elements) that decay over time to radon which, as a gas, can escape through cracks (if it can't escape, it will simply decay further rather than building up as the half life is less than 4 days).
Granite tends to contain more uranium, but various Peak District shales also contain more uranium. Even limestone can contain some uranium (in amounts that vary considerably I think?).
What also matters is the surface area of rock where radon can escape. If you have a large granite body producing lots of radon per cubic metre but there only a limited number of cracks where the radon can escape, then most of the produced radon will simply decay in situ. However in a cave, even if the quantity of radon being produced per cubic metre is quite low, there are often lots of cracks and exposed surface area where radon that is produced can escape.
So it's complicated...
