I went on the self-guided audio tour of the Churchill Bunker at (near?) Whitehall once. In part of the audio tour, when you pass by the small arms lockers, the narrator says something like "if German troops had attacked the bunker, Churchill would have grabbed a weapon and joined the garrison in defending the bunker."
This wasn't presented as an historical "what if?" scenario but as an open-and-shut matter of established fact.
Now, when I complained about this to a friend - I said that this turned the whole bunker tour from a museum into a weird patriotic carnival ride - they pointed out that in 1911 Latvian revolutionaries attacked central London and gunned down a bunch of unarmed British police using automatic weapons, whereupon Churchill apparently took personal command of a platoon of Scots Guards to respond to the attack and was photographed ...
THAT SAID, in 1940, Churchill would have been a corpulent 65 year-old so I find it hard to believe he wouldn't have just got in the way had he actually decided to take part in defending the bunker instead of withdrawing.