I doubt you mean that, but if you do that would be a mistake of the highest order. If Britain wanted to punish Argentina (or 95% of the nations on Earth) it could easily do so with one Astute submarine. As long as the Brits don't try to 'nation build' (they would horribly fail at that since their military is incapable of that) but only needed to do conduct a powerful conventional strike, a single Astute off the coast of Argentina would be an impregnable/invincible/invisible strike platform that could launch land attack and ship attack tomahawks at any Argie asset with near-perfect impunity.
However, the moment they used nuclear weapons on 'the capitols of all nations involved' there would be consequences that are not good. For one, the measure for using nuclear weapons would be drastically reduced. So far nuclear/atomic weapons have only been used twice in anger, and since then there has been no use at all (even though they have proliferated, and some of the countries having them are not necessarily stable nor sane - I am looking at you Pakistan). There has been a very high standard for the use of nuclear weapons, and even when there has been pressure to use them they have not been used since WW2. The moment a 'moral power' like the UK uses nuclear weapons on civilian capital cities ...think about that, nuclear weapons against civilian targets because ships bearing a flag were banned from port ...the whole broth just got changed. What is top stop Pakistan from immediately nuking Delhi the moment they think an Indian counter-attack due to some nonsense similar to what happened at Kargil has gone too far? For that matter, what is to stop them from preemptively nuking the cities? After all, if the Brits can do it? Now, someone can say that because both are nuclear powers MAD will still rule. Alright ...what is to stop China from nuking Taipei with a low-yield tactical nuke?
I am not a dove. Goodness, I actually think Bush wasn't tough enough during the Iraq war (I believe when it is war it is war). However using nuclear weapons against civilian capital cities in an opening salvo would open a Pandora's box so big that it would replace the original myth. And the British would create a situation that the US would be forced to finish (as I used to tell my friends way back during the days we'd go out to nightclubs, don't start a fight I will have to finish). The UK nuking civilian capitals would create a situation that would immediately involve a) the US having to step in as other larger and smaller nuclear powers start acting in uncertain ways, and b) create a precedence of nuclear weapon use that just destabilized the world. Also c) the UK would be challenged again, just not by small weak countries like Argentina. Such an act would be the greatest gift China could get this Christmas, since suddenly all of Taiwan's measures to stop a conventional Chinese attack would pale against the new option of a tactical nuclear attack. After all, if the UK can attack the capitals of several countries, killing millions, because Argentina was acting funny about some island; what about China's case that Taiwan is a 'renegade province?'
Now, ofcourse, in the real world the UK will never nuke a civilian capital (actually, plural - civilian capitals), but even as an internet/FR thought experiment that would never happen. It would be like the US deciding to use nuclear weapons in Viet Nam. Result: The Soviets just started using them in Afghanistan.
The Brits would be starting something they could not possibly be able to finish, and it would be up to the US (yet again) to try and sort out the playground mess. There would also be a lot of 'moral permission' for other global players to use nuclear weapons. For instance, it would be very easy for China to make a comparison between the UK-Argentina situation (and the solution the UK opted for) and the China-Taiwan situation.