As we're about to get a new Prime Minister I thought this would be interesting.
One of the first acts of a new PM is a briefing with the Chief of Defence Staff who will explain to them exactly how much damage a submarines worth of Trident missiles would cause.
When they understand the enormity of this responsibility they are then asked to write 4 identical letters in their own hand, instructing the commanders of the Vanguard nuclear subs on what to do if an enemy nuclear strike has destroyed the UK government and infrastructure.
These letters are then sealed, and escorted to the 4 submarines (one of which is always at sea in case of nuclear attack,) where they are placed in a double safe which can only be opened using 2 keys held by the Captain and XO. When a new PM is instated the old letters are removed and burned, so the PMs decision is never known unless the worst has already happened.
According to a BBC documentary the Chief of Defence Staff lays out 4 options (of course as nobody ever reads them there is nothing stopping the PM choosing to do something else entirely,) they are:
1. Retaliate (this assumes the aggressor can be identified and hasn't already been destroyed by others)
2. Don't retaliate and stand down;
3. The captain may use his or her own judgement;
4. Place themselves under an allied countries command (usually the USA or Australia)
So you're the new PM, assuming Britain has been entirely destroyed, at the time of writing you obviously don't know who by, if its a nation state, a rogue terrorist or a crazed dictator, what would you want the last act of Her Majesties Government to be?