Originally Posted by CosKev3

The best way is to take it off and have a look at the connections,then if they look ok take the alt to a local auto-electrics place and get it tested on the bench

Before you take it off though just disconnect both the small wires off the back and see if the light goes out,the battery light should have an ignition live feed going to it,then before the engine/alternator are turning the alternator earths the light which is how it lights up when you switch ignition on
Then when alternator starts to turn as engine turns the wire from the back of the alternator becomes live,so you then have two lives going to the light,so the light goes off then

Can't really see why your light stays on with no ignition though

Could be a problem with ignition switch on the barrel