Former ministers Nadine Dorries and Sir Jacob Rees-Mogg are among 10 Tories accused of waging a co-ordinated campaign to interfere with a Commons investigation into Boris Johnson.
The ex-PM quit as an MP after a committee found he misled Parliament over Covid breaches at No 10.
In a new report, the committee accused the allies of Mr Johnson of mounting “vociferous attacks” on its work.
But they said the committee was trying to shut down freedom of speech.
The report suggested attempts to “impugn the integrity of the committee” or “lobby or intimidate” committee members could be a contempt of Parliament.
Punishments can range from being forced to apologise to being suspended. However, this would need to be voted for by MPs.
Former Home Secretary Dame Priti Patel and serving Foreign Office Minister Lord Zac Goldsmith were also among the seven MPs and three peers identified as attacking the committee.
The others were Tory MPs Mark Jenkinson, Sir Michael Fabricant, Brendan Clarke-Smith and Dame Andrea Jenkyns, and peers Lord Cruddas and Lord Greenhalgh.
Both Labour and the Liberal Democrats called for Lord Goldsmith to be sacked as a government minister.
Downing Street said Rishi Sunak had full confidence in Lord Goldsmith.
The prime minister’s official spokesman would not say whether Mr Sunak would vote for the report but said MPs would be able to “express their views” and that it would be a free vote – meaning MPs are not told how to vote by their party.
The report, by the cross-party Privileges Committee, said “unprecedented and co-ordinated pressure” was placed on committee members, which although it did not affect the outcome of the inquiry, raised significant security concerns.
It pointed to “disturbing” comments on social media and TV, which it said amounted to a “co-ordinated campaign to interfere with the work of the committee”.
Referencing Ms Dorries’s show on TalkTV and Sir Jacob’s GB News role, the committee added that two of the individuals mounting “the most vociferous attacks” used their own TV programmes as a platform to do so.
The report highlighted comments made by Ms Dorries on TalkTV, when she described the committee as a “kangaroo court”, as well as Sir Jacob calling it “a political committee against Boris Johnson” on GB News.
It also referenced tweets by Mr Jenkinson and Mr Clarke-Smith, who said there had been a “witch hunt” against Mr Johnson.
An email campaign instigated by the Conservative Post website, urging Tory MPs on the committee to stand aside and describing the investigation as “deeply flawed, biased and unfair”, was highlighted in the report as an example of “selective pressure” on committee members.
Lord Cruddas and Lord Greenhalgh, who lead the Conservative Democratic Organisation (CDO) which is linked to Conservative Post, were among more than 600 people who contacted committee members using the email template, the report said.
Lord Cruddas said it was “factually incorrect” to say the emails came from the peers.
The CDO is a vocal supporter of Mr Johnson and grew out of an unsuccessful campaign to give Tory members a vote on reinstating him after he resigned as prime minister.
The report said it would be for the House of Commons to consider what further action, if any, should be taken. It will be debated by MPs on Monday 10 July.
Ms Dorries said there was “absolutely no coordination” in the criticism of the committee and described its report as “bizarre” and “an attempt to close down critical comment and freedom of speech”.
Sir Jacob also accused the committee of “trying to stop freedom of speech”.
Mr Clarke-Smith said he was “shocked and disappointed” to be named in the report, adding that it raised “serious questions about free speech”.
Mr Jenkinson and Sir Michael also defended their previous comments about the investigation.
The committee’s report said free speech was “at the heart of parliamentary democracy”, but some politicians had interfered with disciplinary proceedings set up by the Commons in an “unacceptable” way.
It suggested abuse of committee members could deter others from serving on the committee in the future.
Labour’s deputy leader Angela Rayner described the behaviour of the MPs named in the report as “disgusting” and said the prime minister was still not addressing it.
Commons Leader Penny Mordaunt said the fact a debate had been scheduled on the report showed “how seriously the government takes these matters”.
She added that it was “vital” that MPs were prepared to serve on the Privileges Committee.
The Lib Dems pointed out that four of the individuals named in the report – Dame Priti, Sir Jacob, Sir Michael and Dame Andrea – had recently been put forward for honours by Mr Johnson.
They called for an investigation into whether there was any “collusion” between Mr Johnson and these MPs – and for a commitment to revoking their honours if there was.
Mr Johnson announced he was resigning as an MP days before the committee published its initial findings, branding the investigation a “kangaroo court”.
The year-long inquiry found Mr Johnson made multiple deliberately misleading statements to Parliament about lockdown parties at Downing Street.
It ruled he should have been suspended for 90 days had he remained in the Commons.
The sanction, which was lengthy by recent standards, would have been likely to trigger a by-election in Mr Johnson’s constituency.
The cross-party privileges committee has seven members, four of which are Tory MPs, two are Labour members and one is from the Scottish National Party.