Mr Wragg also alerted Sir Lindsay Hoyle to the allegations, with the Commons Speaker warning ministers that the claims, if proven, would amount to contempt of Parliament.
Sir Lindsay later told MPs that those who work for the Government “are not above the criminal law”.
He added: “The investigation of alleged criminal conduct is a matter for the police and decisions about prosecution are for the CPS. It would be wrong of me to interfere in such matters.”
A Metropolitan Police spokesman said: “As with any such allegations, should a criminal offence be reported to the Met, it would be considered.”
Responding to the claims, Mr Johnson told reporters he had “seen no evidence to support any of those allegations”. Other MPs accused Mr Wragg of exaggerating the issue in a bid to encourage more colleagues to submit letters of no confidence.
However, an MP familiar with the allegations told The Telegraph that the examples included colleagues being threatened with losing access to various local funding pots, including the Levelling Up Fund, Community Renewal Fund and Town Fund.
They also alleged that similar threats had been made during votes on cuts to the foreign aid budget, as well as an attempt by Tory MPs to amend the trade bill to accuse China of committing genocide.
His claims were also backed publicly by Christian Wakeford, who on Wednesday defected from the Tories to Labour in protest over Mr Johnson’s handling of the party-gate scandal.
Speaking to reporters later in the day, Mr Wakeford said he was threatened with the loss of a school in his constituency if he failed to vote in a “particular way” during a debate on extending free school meals provision to cover the holidays during the pandemic.
“This is a town that’s not had a high school for the best part of 10 years, and how would you feel when holding back the regeneration of a town for a vote,” he told the BBC.
“It didn’t sit comfortably and that was when I was really starting to question my place, where I was, and ultimately where I am now.”