The pound has played a starring role in the U.K.’s Brexit drama. Now there is a cameo for the 50-pence piece too.

Roughly one million commemorative 50p coins commissioned to celebrate what some Britons had hoped would be “Independence Day” on Oct. 31, 2019—the latest date on which the U.K. was supposed to have left the European Union—will be melted down, according to the country’s Royal Mint.

U.K....