Boris Johnson is facing twin allegations of a partygate cover-up, with opposition leaders accusing him of “behaving like a tinpot despot”.

The Liberal Democrats claim reports that Downing Street put pressure on Sue Gray to dilute her report reveal an attempt to cover up “lies and law-breaking”.

And Labour is to force a Commons vote on a move by the prime minister to re-write the ministerial code, which deputy leader Angela Rayner claims will “give a green light to corruption”.

Responding to a Sunday Times report on the Gray report, Liberal Democrat Chief Whip Wendy Chamberlain MP said: “This looks like another disgraceful attempt by Boris Johnson and the Conservatives to cover up for their lies and law-breaking.

“The Privileges Committee must immediately look into the supposed interference into the publication of the Sue Gray report. If the government really did alter the report, the British public should be told the truth.”

In its report, The Sunday Times claims: “Sources, both political and civil service, say Gray was lobbied on Tuesday evening to make changes by three senior civil servants.

“They urged her not to publish the names of some of those who had attended the 12 law-breaking parties. Other changes were also requested to passages in the report that made reference to Carrie Johnson, the prime minister’s wife.

“Gray told them to ‘instruct’ her to make the changes – a move that would have required a senior minister to sign off amendments, signalling publicly that the revisions had been made against her will.”

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The report says a senior figure in Downing Street claimed that Downing Street chief of staff Steve Barclay was approached and, after discussions with director of communications Guto Harri, refused to issue the instruction, and Cabinet Office minister Michael Ellis would only carry out the request if ordered to do so by Mr Barclay.

“The result of the standoff was that a number of names were removed, because by then the key pressure had already been brought to bear,” the newspaper claims. “Up to 30 people had been contacted by Gray telling them she intended to name them. In the end only 15 people were named in the final report.”

In response to the report, a Cabinet Office spokesperson said: “We did not change the report in terms of substantive content. The key point that we would say about anything [that suggests] previous copy was substantively edited – it was never shared with Number 10 in advance.”

Labour, meanwhile, has committed to using an opposition day in the Commons to debate ministerial standards after Mr Johnson amended the ministerial code so ministers would not always have to resign for breaching it.

Ms Rayner claimed: “Boris Johnson is behaving like a tinpot despot and is trampling all over the principles of public life.

“Many decent Conservative MPs are deeply uncomfortable with Johnson’s behaviour and they now have the chance to stop his sinister attempts at watering down standards and integrity in our democracy.

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“Serious breaches of the ministerial code must result in resignation, whether they are deliberately misleading parliament, bullying staff, bribery or sexual assault.

“This prime minister simply cannot be trusted to uphold standards in government while his conduct sinks further into the gutter and he gives the green light to corruption.

“It’s time to stop the rot that this prime minister has created at the heart of government and restore standards in public life.”