http://www.ukradon.org/
Kinda difficult to mitigate against in old properties as you can never really get a complete seal on the floor-wall junction and employ tray details like with cavity wall construction, or build in membranes from the outset. But, floors can be dug up, membranes installed (which might coincidentally help with damp/cold floors as insulation can be incorporated too if there’s none already) and sumps/pumps put in.
It really depends on the age of the property if it’s an issue, anything from the last 15 years or more should have been designed with appropriate radon protection. And generally if the house has a suspended ground floor (timber or beam and block) with a ventilated sub-floor void it’s a non issue.
Monitoring devices can be installed, and frequently are to assess radon levels, this is the correct course of action, with any mitigating measures being implemented only after radon levels have been established.
As with lots of house problems, VENTILATION is key.