What has to be considered under this scenario is that if the UK were hit by Soviet tactical nuclear weapons, they would respond on Russia with a Polaris launch (Moscow Option). Not being able to distinguish this from a US launch and possible decapitation first strike, the Soviets would have to launch - triggering a full scale exchange.
It;s a good thing all UK Polaris and Trident missiles have an electronics module installed installed that allows the CIA to disable all those missiles, even if the UK missile submarines are far out at sea and submerged.