I've just moved into a house about 3 weeks ago and the central heating
does not work. I've not owned a house before so I'm a real novice.

Probably the pump. Could be the zone valve, although they might not have
bothered to fit one. Even if they have, the controls should have been wired
so that the pump only fires when the valve is detected to be open, but they
might not have bothered to wire properly.

Christian.