The only major loss I recall reading about from back then was a destroyer taken out by an Exocet missile. But the British armed forces of 2012 aren't the armed forces of 1982. The fight would be far more even if Argentina attacked this time around. I suspect they'd be begging for help from the U.S.
If you are talking about the General Belgrave, that was an Argentinian cruiser - it was torpedoed by a British nuclear submarine. This is the only ship ever sunk by a nuclear submarine in world history. Well, I mean by torpedo - the U.S. sank a hawaiian fishing boat by violently surfacing right under it.
The ship badly damaged (and IIRC later scuttled) by the Exocet was a British transport & supply vessel.
An Argentinian submarine was bombed into oblivion when it was discovered docked at one of the Falkland Islands - on the surface in plain sight!!!
Another little bit of military trivia is that this was the only wartime use of the big delta-winged British Vulcan bombers before they were retired.
I read an account of that war by an Argentinian air force officer who said that their air force generally considered the Argentinian foot soldiers to be cowards and generally worthless in every way.