Way back, during the cold war, I was at a museum in England where they had an exhibit about the cold war. Part of the exhibit was a graphic depiction of the world's nuclear arsenals; The Soviet and US arsenals were huge, with tens of thousands of warheads each; Britain had about 300. A chap came up, took a look at the graphic showing the UK with less than 1% of the Soviet arsenal, and started into a rant about how the Russians wouldn't take such a tiny ability as ours seriously as a deterrent.
I asked him to name the 301st largest town or city in the USSR, and imagine what the country would be like if all the bigger places had been destroyed, and he shut up.
One sub may not be able to destroy half the word, but if it can wipe out the hundred largest cities in an enemy nation, and still have a reserve in case you don't stay down, it is more than enough to make them think twice about provoking you to use it.
Britain's nuclear deterrent (and France's) presented the Soviet Union with a problem. Soviet planners might argue that the USA would be unwilling to risk a full nuclear exchange with the inevitable destruction of every major US city and millions of casualties just to save western Europe.
The fact that Britain and France had their own, independent, systems meant that even if the USA backed down there was still a strong probability that the USSR would be wrecked.
This. One of the prime aspects of a deterrence system is that your enemy knows about it and believes it will be used.