“They show Churchill with what looks like a .45 auto. I can’t say for sure that he never had one but it would look a lot more authentic if he was using a broomhandle Mauser.”
According to reputable written sources his pistol of choice was a 1911 .45ACP.
I can’t say for sure that Churchill never used a M1911 but I have never read of his having used one. The gun most associated with him is certainly the C96 “broomhandle” Mauser. He also apparently used a couple of Webley revolvers at various times.