The UK has a decentralised system for government statistics, which means you will find statisticians working across a wide variety of government departments rather than in one place. Very often these statisticians work closely with (but independent of) policy staff in the department. The Government Statistical Service (GSS) is the umbrella organisation which brings together all statisticians across government; it is headed by the National Statistician.
The largest employer of statisticians in government is the Office for National Statistics (ONS). The ONS is the country’s largest producer of statistics and is responsible for collecting and publishing a wide range of statistics.