Battery Light Illuminated After Ignition Switched Off?

I own a 1994 Mk3 Cavalier 2.0i CD. Very nice car. The problems began yesterday when, whilst a mile from home the (!) light and the battery light on the dashboard came on. Scary! Then after going through a set of traffic lights they went off, only to come back on again. And go off, and so forth. Until about 30 seconds from home they went off, and even after idling the car in the car park for 5 minutes they never came back on.
Fast forward to this evening. I went out to the shops (5 mile round trip to Tesco and back). The lights went out as usual when the car was turned over, and the journey was completed satisfactorily. However, upon getting home, when i switched the engine off the battery light came back on (as well as the (!) light being illuminated very dimly), this was accompanied by a clicking noise from the central locking. When I put the ignition back on, to bring all the dash lights back up, the battery light no longer illuminates. The car fires up normally, and no warning lights light up.

Any ideas anyone? Cheapest idea to fix first would be most appreciated, obviously!!