Update: As several people have pointed out, the original headline on this post, "Churchill might not have put up with that, but he was pedantically opposed to this" did not contain an infinitive (in this case, to oppose). I've changed it to reflect that. There are lots of fake rules of grammar that are bandied about as truths. One is that you can't end a sentence with a preposition. (This results in sentences such as "I don't know to which store I am going" instead of "I don't which store I am going to.") A Winston Churchill line is often used in debunking this: “This is the sort of English up with which I will not put.” (There's a question about exactly how he phrased it; see this for more.)
But Churchill apparently clung to another false grammar rule -- that you can't split infinitives. (This blind opposition can result in awkward sentences like "He was opposed pedantically to this.")
Last night, I started reading Rick Atkinson's Day of Battle, a book about the Allies' campaign in Italy during World War Two. In the prologue, Atkinson writes about Churchill's May 1943 trip across the Atlantic to the United States for a two-week conference on war strategy. During the five-day journey, Churchill "rebuked those unblessed with his fluency by reading aloud from Fowler's Modern English Usage on the 'wickedness of splitting infinitives and the use of very instead of much.' " I checked the notes, Atkinson was quoting from Churchill: Taken from the Diaries of Lord Moran. Moran was Churchill's personal physician.
So much for Churchill being a paragon of common-sense English. (I have a copy of the 1965 revised edition of Fowler's book, and it does seem to look down on splitting the infinitive.)
John McIntyre of the Baltimore Sun said this about the no-split-infinitive rule: "A hoary shibboleth. If your English teacher warned you off this, she was wrong. If your first editor forbade this, he was wrong. If you own a book that prohibits this, get rid of it." And Craig Lancaster of the Billings Gazette has a whole slew of links about the issue here.