This may be my simple mind missing something.
But HMG keep saying how they respect the Falkland Islanders right to self determination, if so would it not be more benificial to grant the Islands Independance, then let the Falklands join the Commonwealth or rejoin the UK.
That way the Falkland Islanders get to do what they want and remain British, and the Argentinian Goverment would have no grounds to claim sovereignty, and the UN would be happy as well?