What no, I'm talking of the 1830s. The British came back and expelled the Argentinian settlement, and settled back in.

They came back because the Argentinians occupied it.

I see two different reasons for a claim for Argentina: that they settled when there was no permanent occupation, like the French and the British did originally, and that they inherited Spain's claim (who purchased the French settlement) following their independence from Spain.

My post was mostly going for humour, but if we're looking at it a bit seriously, England's claim is a colonial one, a legacy from a bygone era. They will inevitably have to cede the islands.