[UnderseaLcpl]

I'll bet anything that the "un-named second" is the President of the U.S. or a U.S. D.O.D. official. At the very least, it would have to be a foreign official that is closely aligned with Britain. Britain, and what remains of her empire, simply do not have the landmass available to survive a nuclear first-strike. Even if Britain's government were to survive a nuclear attack, they would not likely have communications capabilities to issue retalitory instructions.
Of the three large countries that would act in support of Britain's interests, only one is nuclear-capable, the U.S. The U.S also has dead-man trigger devices for their virtually untargetable SSBNs.
The U.S is also distant enough from the former Soviet states (and Russia itself) and the Middle East to allow enough time to decide whether a retalitory strike is warranted, or if the attack is a localized terrorist action.

In the event that both the un-named U.S. official, and the Prime Minister were both killed, before a launch decision could be made, the likely target is Russia and her former sattelite states. They are the ones most capable of launching such a comprehensive nuclear attack.