Backbencher Julian Sturdy had begun the trickle of fresh voices demanding Mr Johnson’s exit after the damning inquiry from the senior civil servant was published on Wednesday.
Meanwhile, Downing Street’s chief of staff said the Prime Minister has made a “significant change” to No 10 by shaking up his team and apologising for the lockdown-busting events.
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Steve Barclay said he and Mr Johnson were both “shocked” and “appalled” by the report’s findings after it was issued on Wednesday, nearly a week after the Metropolitan Police concluded its investigation.
The force handed out 126 fines for rule breaches in No 10 and Whitehall, with the Prime Minister receiving a single fixed-penalty notice for his birthday party in June 2020.
In a statement, Mr Simmonds, the MP for Ruislip, Northwood and Pinner, said: “I listened to what the Prime Minister had to say at Prime Minister’s Questions, his statement and the 1922 Committee yesterday following the publication of the Sue Gray report.
“Having reflected on what he said, and the views of the constituents and my Conservative association, it is clear that while the Government and our policies enjoy the confidence of the public, the Prime Minister does not.
“Accordingly, it is time for him to step down so that new leadership can take forward the important work of the Government in ensuring that our people and country prosper.”
Minutes earlier, Mr Baron accused Mr Johnson of misleading Parliament, and said he “no longer enjoys my support.”
“Given the scale of rule-breaking in No 10, I can not accept that the Prime Minister was unaware,” he said in a statement on his website.
“Therefore, his repeated assurances in Parliament that there was no rule-breaking is simply not credible.
“Having always said I would consider all the available evidence before deciding, I’m afraid the Prime Minister no longer enjoys my support – I can no longer give him the benefit of the doubt.”
Former minister Tobias Ellwood has also been repeating his challenge to Tory colleagues to oust their leader.
Mr Barclay, the Chancellor of the Duchy of Lancaster, said he and Mr Johnson were “shocked and appalled” by Ms Gray’s report, in particular around how cleaning staff were treated.
He told Sky News: “We had an all-staff meeting yesterday in Downing Street further to that.
“It is why we’ve had so many changes in terms of both myself going into Downing Street, the permanent secretary, a new director of communication, a new principal private secretary, it’s why we put procedures now in place.
“We were appalled. That’s why the Prime Minister apologised, it’s why he went to the House of Commons. He said how humbled he was to read about what had happened.”