I mean, I know that Argentina has claimed the islands as long as it has existed, but specifically, in early 1982, were there any signs that military action was possible/probable, or did it come as a surprise to all concerned on the UK side?
Odd reason I'm asking; I write a blog on Formula One history and at the start of the 1982 season, Argentine driver Carlos Reutemann suddenly quit the (British) Williams team with whom he had come within an ace of winning the championship the previous year. No reason has ever been given, but the rumours were "political" fallings out with team boss Frank Williams, though whether of the international or internal variety is never specified.
Reutemann quit shortly after the Brazilian GP in late March and the Argentine invasion took place on the weekend of the following race in the USA; the Argentine GP itself was due to take place in February but had been cancelled due to the economic situation.
It wasnt entirely out of the blue, but neither was it obvious. There were signs, like Argentine landing 'scrap metal merchants' on South Georgia, and apparently making 'murmering' noises at the UN (although I'm not entirely sure what they were). The difficulty is in seperating intent from mere suggestion. So whilst trying to talk their way into an agreement they may have made hints that they would take direct action, but its not certain whether the people suggesting that actually believed it would occur or were privy to any inside knowledge. I think you can say Argentina suggested something, and then that something came true.
The time from decision to invasion was quite short. 4 months or so from the moment it was discussed (and decided) by Galtieri and Admiral Anaya in early December '81 (the invasion around 2nd April '82). Argentina didnt anticipate the reaction it got and so had planned for a 'light' invasion. There were numerous signs that Argentina was testing the UK, but nothing that clearly proved an invasion was imminent. However, Captain Nick Barker of the HMS Endurance had a long and extensive knowledge of the waters, the Argentines and the whole situation. He advised his superiors many times that something was coming but was largely ignored.
Reutemanns resignation fits the timeframe, the invasion planning was under way in Jan 1982. So its possible he was secretly informed that a 'spat' was coming up. However, the Argentines fully expected to get away with it and the UK to just fold and give up the Falklands. So it would be unusual to say 'ok Carlos, we're gonna invade the Falklands, but we fully expect the Brits to give in with barely a grumble, so you'd better quit your team'. You would only suggest that if you believed that a long hard grudge match was going to unfold. So I'd be inclined, without any direct evidence, to say that this may just be a falling out. Relations at the time were frosty between the countries, but not very much in the public eye, until about 1 April.
The threat of invasion was certainly discussed by the previous Labour government. In 1976 the Prime Minister Jim Callaghan spoke of the threat, especially as there were the potential of finding oil fields in the vicinity. In 1977 a Joint Intelligence Committee report concluded that the Argentine's could take the islands without a shot being fired. Thy British government even conducted secret military manoeuvres as a prelude to sovereignty talks that September.
Source: Tony Benn: Against the Tide: Diaries, 1973-77
There is a good witness seminar on the King's College London CCBH oral history programme. John Nott, then minister for defence said "so far as deterrence was concerned in those far off Islands, I don't think I ever thought about it." Richard Ned Lebow argues in "miscalculation in the South Atlantic :the origins of the Falklands War", (Journal of Strategic Studies vol 6, 1, 1983) that Britain didn't expect Argentina to invade and Argentina didn't expect Britain to fight. They thought Britain would negotiate and that possession of the islands would help them.
There are two relevant factors which nobody has mentioned yet. First is the fact that even though the Argentinean leadership was intending to invade some time in 1982, they brought the plan forward as a result of the landing of the scrap metal merchants on South Georgia. This turned out to be a major misstep since it gave Britain enough time to send the task force and retake the islands just days before the harsh South Atlantic winter set in. However the Argentines thought the indecisive way the British had dealt with the unauthorised landing of the scrap merchants, and the fact HMS Endurance had been sent from the Falklands to South Georgia, indicated that the chance of a British response was slight. The decision to invade was taken on 26th March (according to Max Hastings and Simon Jenkins in The Battle for the Falklands) and it went ahead on 2nd April. The invasion therefore came as a surprise to many Argentineans.
On the other hand, the British were aware enough of the coming invasion to warn the governor of the Islands, Rex Hunt and dispatch a nuclear submarine south on 29th. The First Sea Lord, Admiral Sir Henry Leach, had had several days to consider the feasibility of sending a task force and so was able to assure the Prime Minister on Wednesday 30th that such an operation was possible and the task force could be made ready to sail by the weekend.