Just had a couple of early starts and while it was cold and damp the battery light stayed on. It went off over about 3000 revs but stayed on the rest of the morning. There's was a bit of a burning smell (a bit clutch-like), too. Any ideas? Slipping belt maybe? How do I get in there?

Sounds like the alternator is U/S you should check the connections and wiring first for any signs of burning/shorting out.