I do not know if Winston Churchill had a parrot or not (he seems to be a animal person though). I do not want to get into details but some people recently even have tried to twist the views onto Winston Churchill. That said I am surprised Andrew Jackson and Dolly Madison did not make the famouse people with parrots. I am trying to find out if Dolly Madison's parrot outlived her. Supposedly Andrew Jacksons bird outlived him and had to be escorted from the funeral when it screamed obscenities (I do not know if that is true or not though).
You might find this link interesting: Polly Want a WHAT?! Andrew Jackson's Pet Parrot