The W. C. Fields version of this story is definitively attributed, and the evidence would seem to suggest that the Churchill story is also true.
The Fields version almost certainly predates Churchill. It comes from the film It's a Gift, released in 1934; Bessie Braddock didn't enter Parliament until 1945, and most versions agree that it was she who was Churchill's 'victim'.
Not even Fields (or his script-writer, Jack Cunningham) was the originator of this stinging witticism however. The Quote Investigator (QI) cites several other examples, the earliest of which is this one dating from 1882:
"The great A. B. was tremendously jostled the other day in going down to the House. A. B. didn't like it. "Do you know who I am?" he said; "I am a Member of Parliament and I am Mr. A.B." – "I don't know about that," said one of the roughs, "but I know that you're a damned fool." – "You're drunk," said A.B.; "you don't know what you're saying." – "Well, perhaps I am rather drunk to–night," said the man, "but I shall be sober to–morrow morning; but you're a damned fool tonight, and you'll be a damned fool to–morrow morning."
This came from the diary of "the English raconteur Augustus John Cuthbert Hare", who doesn't spell out the identity of "the great A. B."; but in another exchange that the QI has traced, the butt of the joke was Sir Ellis Ashmead–Bartlett – the American–born Conservative member for Eye, 1880–5.
© Haydn Thompson 2020