Downing Street spent £130,000 of public money on lawyers to criticise the Commons probe into Boris Johnson ’s behaviour.
On Friday, top QC Lord Pannick claimed the Privileges Committee is adopting an "unfair procedure" and "fundamentally flawed" approach.
Downing Street commissioned the legal advice from the crossbench peer and published it on the Government website on Friday in a highly unusual move, drawing accusations the outgoing Prime Minister is attempting to "intimidate" the committee in a bid to clear his name.
The Guardian first reported on Friday that a £129,700 contract for legal advice was awarded last month.
Details published on the Government's website on Friday appear to show that the Cabinet Office awarded a contract of £129,700 to the law firm that instructed Lord Pannick for four months of "legal advice".
Downing Street argues that the inquiry by the Privileges Committee relates to the Prime Minister's conduct, raising issues that have a broader consequence for all future ministers.
Although Mr Johnson is due to leave No 10 next week, the Privileges Committee is going ahead with its inquiry into whether he committed a contempt of Parliament by telling the House on several occasions that there were no lockdown-busting parties in Downing Street.
Lord Pannick, who previously acted against the Government over Brexit in the Supreme Court, argues in the 22-page document that "the committee has failed to understand that to prove contempt against Mr Johnson, it is necessary to establish that he intended to mislead the House".
"In our opinion, the committee is proposing to adopt an approach to the substantive issues which is wrong in principle in important respects, and the committee is also proposing to adopt an unfair procedure," his legal advice states.
"But for Parliamentary privilege, a court hearing a judicial review application brought by Mr Johnson would declare the committee's report to be unlawful."
He also suggested that a failure by the committee to make an explicit distinction on whether Mr Johnson misled MPs intentionally could have a "chilling effect" on parliamentary debate, with MPs fearful of mis-speaking.
A spokesperson for the Privileges Committee previously denied there had been a change to the rules or to terms of reference after allies of Mr Johnson claimed it used to only matter whether the House had been misled deliberately.
The Prime Minister's intention is not relevant in deciding whether a contempt has been committed, the committee has made clear.
Welsh Secretary Sir Robert Buckland denied allegations by some allies of Mr Johnson that the Commons committee has deliberately chosen its terms to ensure that the Prime Minister is found guilty.
He said he would advise the new prime minister against "any suggestion that somehow the committee should be impeded or prevented from carrying out its inquiry".
However, the former justice secretary said it was "entirely legitimate" to have a discussion about "the precise parameters" of the probe.
Labour MP Chris Bryant, who chairs the Privileges Committee but has recused himself from the partygate inquiry, dismissed the Government-commissioned legal opinion by Lord Pannick as "disgraceful bullying".
"Lord Pannick's bizarre 'opinion' has no formal status and is wrong on several counts," he wrote in a series of tweets.
"You would have thought that Boris Johnson would want to clear his name in front of the Privileges Committee instead of trying to intimidate it.
"There is no danger of ministers being cowed by this inquiry - although of course it would be good if they were careful that what they say to Parliament is true and accurate - as the House will always recognise an honest mistake quickly corrected.
"It's time this disgraceful bullying stopped. Let's hear and see the evidence. If Johnson has a good case to make, he'll be vindicated. If not, he should take his punishment."
Mr Bryant noted that House of Commons processes allow ministers to correct the record if they mis-speak.
It comes as the Telegraph reported that the inquiry could face being "watered down" under a Liz Truss administration, with the newspaper citing some of the allies of the Foreign Secretary who have launched fresh attacks on the committee.
The Liberal Democrats had earlier demanded to know how much taxpayer money had been spent on commissioning the advice for Mr Johnson.
Lib Dem spokesperson Christine Jardine said: "People are tired of these expensive attempts by this Government to manufacture ways for Boris Johnson to wriggle out of any consequences of his actions.
"The Government must fess up to the cost of this legal advice and stop expecting the taxpayers to pick up the tab for Conservative sleaze."
Thangam Debbonaire, shadow leader of the House of Commons, told BBC Radio 4's World At One programme: "This current Prime Minister needs to be able to show - and the investigation's got to be free to investigate this - that he corrected the record at the earliest possible opportunity.
"Otherwise, I'm afraid to say, it just looks like the sleaze and the lies and the cover-ups that people have described it as."
The Covid law-breaking parties in Downing Street were among the scandals that forced Mr Johnson's resignation as Tory leader.
With his refusal to rule out a political comeback, the committee's investigation threatens to further tarnish his legacy and could impact his future as the MP for Uxbridge and South Ruislip.
If he is found to have lied to Parliament, Mr Johnson could be suspended from the Commons or even kicked out in a by-election after a recall petition.
A spokesperson for the Privileges Committee said: "The committee notes the publication of Lord Pannick's advice relating to its current inquiry. The committee will meet in due course to consider in detail Lord Pannick's arguments and will issue a response when it has done so."
Lord Pannick declined to comment on his legal opinion.
