Just noticed my battery light showing when car is running. Is this indicating a alternator that's not charging the battery...

Yup, afraid so. Check the belt tension, as it could be that, which in turn wont turn the pulley on the alternator enough to charge the battery. otherwise check the alternator connections at the back, and give them a clean. Failing that, get a voltmeter on the bugger everywhere to see if the battery is being charged or not. Across the battery should be over 13v when running. Anything below that, and the alternator isn't charging, which will most likely be a duff alternator.

You may also check the lenght of the brushes attached to the relay, in time they wear out.

Hi mate
Probably an alternater belt.
If it is all cracked on the inside when you take it off, it needs changed.
It will also squeal like a banshee if its loose.
Cheers Mark.

Also check for connection problems with spade clips, earths and bypass resistor on the dash panel.