I'm wondering if there is a difference between UK and US construction methods. That document seems to suggest that UK houses usually have empty space under their ground floors; is that true? This seems to be common practice only in older US houses built before the mid 1900s, usually with wooden ground floors.
In the US, the lowest floor (basement, or ground floor in a house without a basement) is usually a reinforced concrete slab poured over gravel over dirt. In areas with lots of rain (e.g., the east coast where most of my family lives, but not here in California) houses with basements in flood-prone areas often have sump pumps. A sump (a hole dug into the slab to below the gravel layer) accumulates water from storm ("French") drains buried around the outside periphery of the house, and a pump periodically empties the accumulated water from the sump into the sewer system or simply to the street. Any water in the basement itself can similarly be drained into the sump to be pumped out.
When my parents discovered high radon levels in their basement, they had a contractor cover this sump with plastic and install a continuous pump to exhaust the air within the sump. Although there's no actual gap between the slab and soil, the gravel between them is porous enough for radon that would otherwise diffuse through the slab and into the house to be drawn into the sump and exhausted outside.
It is kind of surprising that radon can diffuse through solid concrete quickly enough to get into a house before it decays (3.8 day half life) but apparently it does.