I doubt it. A mate, who's a politcal scientist of sorts in US, made an interesting point - if they had waited, we might well have given it up, as we were giving up small distant patches at the time - Zimbabwe (1980), Vanuatu (1980), Belize (1981), and Antigua and Barbuda (1981).
And the UK and Argentina signed a 1968 memorandum aiming to recognise Argentine sovereignty, subject to future safeguards.
But, with military spending on the rise in the UK, they might have missed the boat already ...