The person leading the effort is Victoria Cleland, 46, the bank’s chief cashier, whose signature is on every new £5 note. (She said she signed her name carefully and neatly.) Ms. Cleland, who studied philosophy, politics and economics at Oxford before getting her M.B.A., said the polymer notes, post spin cycle, had proved far sturdier than their paper counterparts.

“The paper notes get quite soggy and disintegrate, whereas the polymer notes retain their shape and don’t get crumpled,” she said in a telephone interview. Last year, 21,745 notes of all denominations were returned as mutilated, the central bank said.

She said the notes had also been carefully tested in the laboratory by health and safety experts to assure that pets or children accidentally chewing on them would not become ill. “A number of notes get returned each year and are chewed by pets, including parrots,” she said, before quickly adding: “We wouldn’t encourage people to swallow the notes.”

Bank notes are important symbols of national identity. And the decision three years ago to replace the social reformer Elizabeth Fry with Churchill spurred some loud protests, since the queen would be left as the only female figure on British currency.

After the dissent, the bank decided to introduce a polymer £10-note featuring the author Jane Austen, who will replace the scientist Charles Darwin when that note is introduced next summer. The choice was a sign of “sense and sensibility,” the former chancellor of the Exchequer George Osborne wrote on Twitter at the time.

On Tuesday, Mr. Carney extolled Churchill as “one of the greatest statesmen of all time.” When Mr. Carney’s predecessor, Sir Mervyn King, first announced plans for the new Churchill note three years ago, he mused that the new £5 notes could be eventually referred to as “Winstons” and said it was appropriate that Churchill should be on “what is probably our most popular note.” Churchill’s words — “I have nothing to offer but blood, toil, tears and sweat” — appear on the bill.