This situation is a 'win-win' for everyone in my opinion.
Argentine politicians get to trot out the vote winning desire to re-capture the Holy Land, without ever actually having to do it.
Cameron gets to act the national hero.
RN gets to re-emphasise the fact that should a small, sparsely populated, water bound, distant piece of real estate need defending then a task force did it last time. In the absence of any obvious examples of 'the next one', 'the last one' will do.
RAF gets to hang onto a few more Typhoons and their crews.
The army hangs onto a few more troops, because for every one deployed you need another four in the cycle.
Wills get his OOA.
Obviously we quite reasonably think that the Argentines cannot take the FI by force because we have infantry and AD aircraft there. To go completely off track - the question this raises for me is why we insist on maintaining our own amphibious capability if it's so damn easy to defend against?
In fact a reasonable exam question to show how far we've sunk would be to ask the question, could we take the FI back from ourselves?
To summarise, I really don't see hostilities happening because the status quo suits all players bubbling along like it is.