If the entire Royal Family and every serving politician had been killed in one gigantic raid nothing would have changed. The country and the Empire/Commonwealth would have gone into mourning but would have carried on fighting. There was already 100% determination in Britain in 1940 to see things through to the end. New leaders and a new Monarch would have been in place quickly and it would probably have very little effect on the course of the war apart from after Victory a few more Nazis swing on the end of a rope.
If the King is killed then the next in line to the throne becomes monarch. That would have been Elizabeth our current Queen, if both Elizabeth and her sister Margaret had been killed in the raid then succession would have gone to Georges brother Prince Henry Duke of Gloucester.
The Houses of Parliament were heavily bombed and the Commons chamber was destroyed unfortunately all the politicians were saved
