Referendum
Ah, yes, quite a good idea...but the GoA are not obliged to grant a referendum to the Bennies, now, are they?
Another clever (and somewhat ironic) legal device would be for the UK to grant the Falkland Island independence after an internationally adjudicated plebiscite, with their legal person defined under Montevideo Convention on Rights and Duties of States 1933, Art 1. (ie permanent population, defined territory, government, and capacity to engage in international relations) Immediately on granting independence (or Dominion status) the UK and FI governments would ratify a mutual defence and assistance treaty. [This is similar to the creation of Belize]. Of course, few South American countries (with the exception of Chile) would recognise this new state, but who cares? The Falkland Islanders would have 'self-determination' as required under UN Charter Art 1(2) and subsequent Decolonisation conventions.
Confusingly, the first colonists in East Falkland were French, in 1764 - who then sold their settlement to Spain in 1767. British occupation of West Falkand comemnced in 1765, which was conquered by the Spanish in 1770 and then returned in 1771. The British abandoned the settlement in 1774, but left a plaque confirming that it remained British (actually English) territory and not terre nullis. It then gets complicated. Argentina (as is) declared independence from Spain in 1811 and took formal possession of the islands in 1820. The Colonial Office, being on the ball, protested some 9 years later. In 1831 a USN ship evicted the Argentine settlers in reprisal for actions taken by the Governor and in 1833 the British captured the island and have remained there ever since, apart from a brief interregnum in 1982. British possession is based on the principle of conquest, which is upheld by international law. Simples!
Oh, and one final point, it is accepted point of international law that a state (in this case the UK) is entitled to rely upon the right of self defence even when its possession of the territory in question is subject to controversy
Stick that up your Junta!