Why bother? Can you really conjure up a scenario where the US would attack us?
I can't conjure up a situation where any sane person would attack us with nuclear weapons, nor can I conjure up a situation where any insane person would not attack us with nuclear weapons because we may fire back.
The most likely use of nuclear warheads would be in some form of asteroid deflection, however Trident missiles, and Thatcher-class submarines, won't help there.
Besides the real threat is the French.
And how would refugees manage to make it all the way to Russia, let alone China?
You may note that refugees reach europe from Africa and the Middle East. After a nuclear attack - when UK citizens survive (which they will) - the best hope for those people is to
1) keep the damage to the planet to a minimum to maximise survival chances
2) keep the infrastructure of the planet well enough to hope they can be fed, have medical care, and keep law and order
3) Don't be in a situation where British citizens can be blamed by survivors for causing the mess, or causing it to be worse
Whether we have the capability, those aims are best met by not launching.
At any point there are 6 or 7 million British citizens abroad. The PM has a responsibility to those people, who will still be alive after a nuclear attack on the UK. In no way can launching a nuclear missile help any British citizen, either the survivors on the mainland or those abroad. Would British citizens on holiday in Japan thank us if we launched a post-strike retaliatory attack on Beijing, and the fallout hit Japan? Would British ctizens in New Zealand thank us for contributing to the end of the world? Or would our citizens face a lynching? Those on business in Canada may not appreciate a global famine causing them to starve to death.
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I think, looking at a comparative matter to strike fear is not HS2, but our very own Class 142 units....
Didn't we send some to Iran, and then ended up with 30 years of animosity?