Since 9/11 there’s been some speculation about the Succession to the Presidency, if some catastrophe were to strike Washington, D.C. Some even allege that the statute that places the Speaker of the House of Representatives, and the President pro tem of the Senate, in the line of succession, is unconstitutional, for inserting the Legislative Branch into the Executive. And some say imaginable scenarios are so chaotic as not to be remedied by the Constitution or any existing statutes as written.
The Commonwealth Crown, OTOH, has at least several thousand in its line of succession, today scattered throughout the world. (All those listed belong to European families, but many of them live outside Europe – some even in the United States.) If London were wiped off the face of the earth, the Crown would fall automatically by act of law to the next living successor. That person would presumably appear somewhere in Britain, assemble a provisional government from among surviving members of the Privy Council (e.g., former Ministers of The Crown) and representatives of the surviving Hereditary Lords, call a general election having determined there were no survivors of the House of Commons – all of this by way of reassembling Parliament, and parliamentary government, as quickly as possible. That person would also have inherited the Command-in-Chief of the UK’s military, though they would probably only act on the advice of the provisional government.
I would even argue that if by some bizarre catastrophe all the living Protestant descendants of Electress Sophia of Hanover who have never married Catholics, vanished at once, the Crown would automatically fall by Common Law to the senior heir of the most recent Monarch of Great Britain or of England (i.e., before William and Mary), being Protestant and having never married a Catholic. But this is apparently not a universal opinion.
In any event, this would have no affect on the governments of the Commonwealth Realms outside the UK, since their Governors-General and parliamentary governments would continue in office untouched. And if tragedy should strike Ottawa or Canberra (or elsewhere), the Monarch in Britain would probably appoint a provisional Governor General to put things back in order in those countries – maybe even the previous surviving GG, having experience of the job – in the absence of governmental Advice.
As a republic, we are crippled!