I think the Argies lost a few as well...and we didn't need to lose anyone, there was a diplomatic solution in progress, but Thatcher wanted the war to boost her popularity. At the time, almost no-one knew where the Falklands were.
According to someone in the RAF that I used to know who was posted there, the locals in the Falklands hate the military who are there, and treat them like crap. Frankly, I think the Argentinians are welcome to the pointless rocks, and their ungrateful inhabitants. We'll take the saving on defence spending.