battery light on - new alternator fitted

Hello all....Problem...The 'battery' dashboard light stays on when engine is running...AA bloke diagnosed new alternator which was duly fitted. Light still on. Battery producing around 12v when ignition not on....no real difference when engine running. What could problem be? if not alternator, what? I will freely admit to being no kind of mechanic and I replaced alternator the way it came off (I think!)
Any help gratefully received!
PS. Not sure what engine what newly acquired LR is...search for engine number anywhere I can see has so far yielded no result....

I believe voltage at battery with engine running should be around 14v...

Clean your battery terminals, check and clean the earths.

Check the trigger wire on the back of the alternator is connected properly

Hi Tom...yes, think that's meant to be the case and bit perplexed as to why it isn't...AA suggested replace battery as well as alternator but battery-seller tested it and said it was fine....! (though I suppose he would, wouldn't he?!) Thanks for that Steve...though the 'trigger wire' is a bit out of my depth...??!

ignition feed through alt light to alternator, enging not running the alt provides earth so the light illuminates.

the altenator needs rotor feild windings energised to charge, so if the alt light is on and disconnecting the small battery light wire it stays on=short to body or engine earth.

w terminal is tacho rpm counter
ignition on and alternator charging = no potential difference ++light out
ps I'm ****ed, so hope it makes sense!