Although Argentina claimed that the territory should have been originally theirs, it was under Britain's control. What started the conflict seemed to be an act of desperation similar to Japan's action to Pearl Harbor. Due to Argentina's thoughts on the territory being theirs, they launched a suprise attack which wasnt justified. Britain simply defended their territories just as any country would do.
When the Falkland Islands were invaded by Argentina's junta dictatorship in disregard of international law, they committed an act of war and Great Britain was thus absolutely justified in taking all necessary military measures to liberate the Falklands from the invaders. If anything, Britain showed great restraint during the war. Their actions were completely legitimate.