The UK posture (and France's) is not about destroying Russia beforehand.
It is to essentially hurt it very badly it in an counterstrike. The UK has 4 Trident subs.
There are four nuclear submarines – Vanguard, Victorious, Vigilant and Vengeance – carrying up to 16 Trident ballistic missiles. Each missile is capable of travelling at least 4,000 miles and carries three nuclear warheads.
At least one sub is always at sea. 6000km range x 48 warheads would allow targeting major Russian cities in one region (presumably Western Russia - Moscow, St. Petersburg). That kills a lot of people, Trident's goal was set to kill at least 10M Russians:
Secret files from 70s reveal Trident strike needed 'to kill 10m Russians'
But if you add judicious targeting of concentrated heavy industries near those cities, you could knock out oil refineries, steel foundries, central government offices and workers, main harbors and railway nodes (usually near big cities), agricultural supply chain chokepoints, etc. Can you imagine what that would do to an economy and industrial base in the short and medium term? Agriculture nowadays is so resource-intensive that famine wouldn't surprise me one bit.
A much more elaborate and extensive version of the USAF WW2 1943 raid on Schweinfurt's ballbearing factories which was intended to cripple the German war effort by denying it a key ingredient to all engines. That failed not necessarily because it was a bad idea, but because real-world, not theoretical, bomb accuracies were nowhere near sufficient for that goal (the factories barely got hit). Nukes don't have that problem.
Rebuilding could take decades and in the meantime Russia would be knocked out of the great powers league. If you're a rational great power leader, but one one doesn't care about human costs, that's what your calculus is about: "can my country maintain its status and power base after such a strike?". Not necessarily "are we utterly annihilated?"
This might not work as well against the US, which has a larger number of big cities, distributed more widely. But knocking out LA, NYC, Houston and its refineries, other big coastal ones (as per comment), some heavy industrial cities doesn't take that many weapons. And it's hard to see the US coming out very well out of that.
Credible and effective anti-ballistic missile defenses would change those calculations however. ABM defenses might not change matters much in a Russia-on-USA exchange, but the much smaller volume of warheads by the lower-tier countries means that a capacity to knock out say 100 incoming warheads reliably, especially if that protection somehow covered the whole country, puts you in a wholly different ballgame.
If instead of the UK, you started making those calculations with China's 300-500 and increasing nukes, the pain factor and longstanding diminution of the US's industrial power and economy increases many times.
Any of those countries, including China, having a credible first strike capability against the US or Russia? No way. Too many nukes in both.
Also, with some nuclear countries (Pakistan, Israel to some extent, India to some extent), their nuclear threat factor to Russia, and especially the US, is either limited or essentially zero as they have limited or no delivery capabilities with the required range. Being able to move them into range is one benefit of ballistic missile subs, besides stealth and not being easily targetable.