What the civil service is
The civil service is the body of permanent, politically neutral officials who staff government departments in the UK. Unlike ministers — who are elected politicians (or appointed peers) who change when governments change — civil servants remain in post across changes of government, providing institutional continuity and expertise.
The relationship between ministers and civil servants
Ministers are responsible for policy — they set the direction their department will take. Civil servants advise ministers on what is feasible, what the evidence shows, what the consequences of different policy choices would be, and then implement the decisions ministers make. The constitutional convention is that civil servants implement the decisions of elected ministers, regardless of whether they personally agree.
How it is structured
The Cabinet Secretary leads the whole civil service. Each government department (the Home Office, Treasury, Department of Health, etc.) is headed by a permanent secretary — the most senior civil servant in that department. Below them is a hierarchy of grades from deputy director through to administrative assistant.
The independence question
The political neutrality of the civil service is both its strength (consistent, expert advice across governments) and a source of tension. Ministers sometimes accuse the civil service of institutional inertia or of pursuing its own agenda. Civil servants are sometimes accused of being too close to their minister's agenda. Managing this tension is central to how the British constitution works in practice.