I thought I'd post a quick update, after all your helpful advice.
I actually decided to get some binoculars first, as a next step before buying a telescope. I now have a pair of Celestron UpClose G2 10x50s, and have been taking advantage of the cold clear nights we've had this last week.
I saw the Orion Nebula and Andromeda galaxy for the first time (knowingly) - amazing. And got a fantastic view of the Pleiades. I tried to find the Beehive Cluster but got lost - went from Castor, past Pollox, then went awry in a sea of stars. All good fun though.
I also discovered that a friend of mine is a keen astronomer, and he's offered to let me look through his fancy telescopes. That should be very helpful.
Lots to learn!