LONDON—The new, leftist leader of the U.K.’s opposition party, Jeremy Corbyn, on Wednesday made his debut at the weekly grilling of the prime minister in Parliament, known for its rowdy debate and exchange of gibes.

But instead of engaging in the usual mudslinging with the prime minister, Mr. Corbyn told Parliament that he wanted to bring a more demure atmosphere to the session and used measured tones to challenge him on issues like housing and welfare.

Mr....