I like your little cartoon of Blair with implications of Maggie.
Of course, Iran is not a tiny set of islands, nor is its military or government as weak as the Argentinian.
Though, at least we likely wouldn't be
supporting the government that they are fighting against this time!
We watch & support their efforts rhetorically & publically, unless we're officially asked to assist. If we're asked to assist we say "yes, absolutely". Then we work out specifically what they need us to assist with, logistics?, ESM?, Special Ops?, military hardware?, air refueling?, actual boots on the ground?
Show of force doesn't hurt either
The British will likely work this out without resorting to warfare.
Though I'm not surprised it is the first idea that popped into your mind.