The number of British ships sunk is only part of the story, there were 22 ships hit and damaged in total, 23 some say. Some of the damage was minimal, with bombs not exploding and passing right through both sides of the ship, and others were just a few cannon round hits. Most of the ships however took some serious damage. Without a large CV deck and the ability to have a real overhead radar coverage zone, her majesty's navy did the best they could under the circumstances with the Harriers doing that job, and the Aim9L was the real performer IMO, giving the British a weapon that was unmatched by the Argies at the time.
http://www.naval-history.net/F62brshipslost.htmThis gives a pretty good accounting of the ships hit during the war, at least on the British side.
So far as the "nuclear" option, I don't think anyone would accept that Thatcher would even consider using WMD on a country currently engaged in conventional war only.
