It is commonly said that houses constructed in the 1940s to 70s (around 1940 - 1975) may have radon-containing lightweight concrete. However, the levels and any health risks depend on many factors. There is no total ban, but there are guidelines regarding radioactivity limits for new constructions from the late 70s.
The concrete is not "radon-irradiated" - rather, it is made from shale containing radioactive substances (Uranium) which then decay into radium, leading to radon gas. This gas further decays, forming radon daughters that attach to dust and smoke, and can be hazardous to inhale because they emit alpha radiation. Smokers, in particular, have been found to face a significantly increased risk of lung cancer. Additionally, this type of lightweight concrete/blue concrete emits gamma radiation too, but the levels of gamma radiation are usually so low that they do not pose a major health risk, as has been determined.
Search for radon to find more threads about this on the forum, including links to the national radiation protection institute, etc.
Here is one of the links:
http://www.ssi.se/radon/Radon_Blabetong.html
/K