Re: Let's cut the BS. It's about the UK's self image as a "World" power.
"IE A massive willy waving exercise"
To a large (but not entire) degree, yes.
But by your examples, you appear to misunderstand the principle of deterrence. Deterrence applies to any/all weapon systems, but only works if the weapon system is credible and the person to be deterred believes that you will use it.
Fairly obviously, you do not deter terrorists that are hiding within your own cities with city-destroying weapons (ICBM is not a credible weapon for use in this case, therefore cannot be considered to be a deterrent for use in this case)
However, deterrence worked perfectly in the case of the Falklands - hence there was no Falklands War of 1977, when the Argentines made all the same moves to invade the Falklands as in 1981/82, and the British response was to park a SSN in the south Atlantic. This left the Argentine junta in no doubt that the UK would defend the islands, and they were deterred from invading (since the weapon systems deployed to deter them were credible as a means of destroying the invasion fleet, and the Junta believed the UK government would use them).
In 1981/82, the British response to aggression from Argentina was to continue with the plan to sell off both carriers, scrap both the amphibious assault ships, and withdraw the Falklands guard ship without replacement. The logical interpretation was that the UK weren't prepared to fight to stop the islands being annexed. Therefore, the weapons possessed by the UK were irrelevant: the Junta believed there was no political will to use them.
A similar example of deterrence succeeding / failing due to political will would appear to be the invasion of Kuwait: the Iraqi invasion of 1961 didn't happen because the UK chucked in troops and made it clear to the Iraqis that we would fight to defend Kuwait, whereas in 1990, the US (the new 'outside power' dominant in the area) failed to make clear politically their view, and failed to deploy troops, so failed to deter, with the Iraqis thus assumed the US would do nothing.
Whether the UK needs a nuclear deterrent is certainty a point for discussion, however, there would appear to be a political/diplomatic advantage (willy -waving isn't entirely without impact).
It might also be noted that Litvinenko was poisoned by Polonium, an action which is generally held to have been the actions of the Russian state, and this year there has been a reported small scale chemical weapons attack against civilians in the UK, again the action of the Russian state. Given that the current Russian government has been prepared to use two classes of weapons of mass destruction (chemical weapons and radiological weapons) against targets in the UK (though only in very small scale volumes, and has attempted to do so covertly in both cases), one could conclude either:
(i) our deterrent has failed, and is useless
(ii) our deterrent is vital, and possibly the only thing stopping the use or the threat of use of a nuclear warhead against civilian target in the UK
(iii) we were never going to launch a nuclear warhead against an attack of such a small scale, so the deterrent was never relevant in either case, but the world is dangerous and unpredictable, so it might be a good idea to hang on to it, just in case.
So those are at least some possible points of the exercise.