John Bercow has written to the leaders of the three main parties at Westminster to call for an end to "orchestrated barracking" at prime minister's questions.

The commons speaker, who complained about "yobbery and public school twittishness", said he had decided to act after hearing from MPs that party whips have orchestrated a "wall of noise".

In his letter to David Cameron, Ed Miliband and Nick Clegg, revealed to the Independent, Bercow asked the three leaders for their comments on a Hansard Society report which highlighted public unease about the atmosphere in the chamber.

The Independent said the report found that 67% of those questioned felt there was "too much party political point scoring" instead of answering questions. A mere 12% agreed with the proposition that PMQs makes them "proud of Parliament".

The speaker said he did not expect MPs to behave like "Trappist monks" and accepted that often "passions will be aroused" in the Commons. But he added: "There are people who think culturally the atmosphere is very male, very testosterone-fuelled and, in the worst cases, of yobbery and public school twittishness."

Bercow claimed that the whips appear to be guilty of fuelling the atmosphere and disclosed that he has asked the party leaders: "Cut out the orchestrated barracking."

The speaker said he had told the leaders he wanted them to say to their MPs: "I don't want it. I want your support and I'm delighted if when I get up I get a big cheer … But the orchestrated barracking of my opponent is not good for the House and I don't want it to happen and I've asked the whips to monitor the conduct." He concluded: "If that were done there would be a step change within weeks."

The speaker said he had received "anecdotal" evidence of the role played by the whips. He said: "I have anecdotal indications that there is some encouragement. I have had one or two colleagues coming to me and telling me they've had text messages [from the whips] saying: 'Thanks for the wall of noise.'"

Bercow spoke out after he was criticised for appearing to lose his temper recently when he called on Michael Gove to write out lines after the education secretary appeared to be making a lot of noise during a session of PMQs. Defenders of the speaker say he is a reformer who holds the government to account, often by hauling ministers into the chamber to answer urgent questions (UQs). Bercow has granted 165 UQs though he says he has turned down a similar number.

• This article was amended on 18 February 2014 to clarify that Bercow had told party leaders he wanted them to say to their MPs: "I don't want it. I want your support and I'm delighted if when I get up I get a big cheer …". Bercow was not saying that he himself wanted MPs' support.