Boris Johnson is battling claims that Tory critics are facing “intimidation” which could amount to blackmail as part of an effort to prevent him being ousted from office.
Mr Wragg said he had received reports of conduct including “members of staff at 10 Downing Street, special advisers, government ministers and others encouraging the publication of stories in the press seeking to embarrass those who they suspect of lacking confidence in the Prime Minister”.
“The intimidation of a Member of Parliament is a serious matter. Reports of which I am aware would seem to constitute blackmail,” the chairman of the Commons Public Administration and Constitutional Affairs Committee announced at the beginning of a hearing on Thursday.
But Mr Johnson, on a visit to Taunton, said: “I’ve seen no evidence, heard no evidence, to support any of those allegations.
“What I am focused on is what we’re doing to deal with the number one priority of the British people, which is coming through Covid.”
He said he would “of course” look for evidence to support the allegations, but No 10 suggested there were no plans to launch an investigation as demanded by Labour.
Mr Wragg is one of a handful of Tory backbenchers to have said publicly they have submitted a letter to the chairman of the backbench 1922 Committee, Sir Graham Brady, calling for a no-confidence vote in Mr Johnson’s leadership.
He said the conduct of the Government Whips’ Office threatening to withdraw public funding from MPs’ constituencies may have breached the ministerial code.
Commons Speaker Sir Lindsay Hoyle said it could be a contempt of Parliament to obstruct MPs in their work, adding that MPs and their staff are “not above the criminal law”.
“While the whipping system is long-established, it is of course a contempt to obstruct members in the discharge of their duty or to attempt to intimidate a member in their parliamentary conduct by threats,” he said.
Christian Wakeford, the MP who defected from the Tories to Labour in protest at Mr Johnson’s leadership and the row over Downing Street parties, said he was threatened about the loss of a school in his constituency if he did not toe the line.
Speaking to BBC North West, he said: “I was threatened that I would not get the school for Radcliffe if I did not vote in one particular way. This is a town that’s not had a high school for the best part of 10 years.”
A Labour source said the vote in question related to free school meals.
But Culture Secretary Nadine Dorries sought to dismiss Mr Wragg’s allegations, telling BBC News: “That is nonsense because that is not how government works.
“It is just attention-seeking behaviour from William Wragg who has been a constant critic of the Prime Minister, who delivered us the greatest majority since Margaret Thatcher.”
Tory MP Michael Fabricant, a former whip, also described Mr Wragg’s comments as “nonsense”.
“If I reported every time I had been threatened by a whip or if a whip reported every time I had threatened them, the police wouldn’t have any time to conduct any other police work,” he said.
Douglas Ross, the Scottish Conservative leader who is among those to demand Mr Johnson’s resignation, told ITV Border the allegations are “serious” and should be “properly investigated”.
Scotland’s First Minister Nicola Sturgeon said it would be “corruption” if investment was being held back from the constituencies of Mr Johnson’s critics.
The Metropolitan Police said they would consider any complaints made to officers.
“As with any such allegations, should a criminal offence be reported to the Met, it would be considered,” a spokesman said.
Mr Wragg’s dramatic intervention reignited the controversy over Mr Johnson’s future just as the mood at Westminster appeared to be calming.
The defection of Bury South MP Mr Wakeford to Labour on Wednesday appeared to have led some of the Tories agitating for Mr Johnson to go to pause as the party rallied together.
Tory backbencher Andrew Percy told BBC Radio 4’s Today programme: “It’s kind of made people a bit more relaxed. It’s calmed nerves.
“I think people have recognised that, actually, this constant navel-gazing and internal debating is only to the advantage of our political opponents.”
But influential backbencher Steve Baker said it looks like “checkmate” for Mr Johnson over the “appalling” allegations of rule-breaking parties in No 10.
Mr Baker, the ringleader of efforts to oust Theresa May over Brexit, told the BBC’s Political Thinking podcast: “We didn’t make Boris Johnson Prime Minister for his meticulous grasp of tedious rules but this is appalling and the public are rightly furious.”