Some numbers....

Background radiation varies across the UK, from under 0.2 mSv/year to
over 0.4 mSv/year (milli Sieverts per year, a measure of exposure).

see http://www.darvill.clara.net/nucrad/sources.htm and countless other
sources.

The Environment Agency will not give a permit to a waste facility that
exposes the public to 0.3 mSv/yr or higher, and expects typical exposure
to be 0.02 mSv/year.

In other words typical exposure will be one tenth or less of the
background radiation, or about 1% of the total radiation exposure of a
typical UK resident.