Mr Sunak has been accused of “running scared” of Monday’s vote on the damning report which found Mr Johnson lied to parliament, as the PM tries to distance himself from the scandal.
But the prime minister has an even lower approval rating among Conservatives who backed the party at the last election than Mr Johnson.
Mr Johnson has a net approval rating of 14, compared to only 7 for Sunak among those who voted Tory in 2019, according to the YouGov survey for The Times.
Mr Sunak is more popular among the wider electorate, however, with a net approval of -23 compared to Mr Johnson -39. Some 61 per cent say Mr Johnson was a bad PM per cent, with 42 per cent saying Mr Sunak is doing badly.
The PM has refused to say whether he will take part if there is a showdown vote on the privileges committee report on his predecessor’s conduct – but is expected to skip the debate and vote.
Labour leader Sir Keir Starmer said Mr Sunak should “show us where he stands” on the issue after the committee concluded that Mr Johnson should have faced a 90-day suspension for repeatedly lying and being complicit in a campaign of intimidation against the panel.
Mr Sunak claimed his reticence about giving his verdict on the report’s conclusions was because “I wouldn’t want to influence anyone in advance of that vote”.
But publicly backing the report and its sanctions could risk deepening the Tory civil war between Johnson loyalists and his own administration. The PM told ITV’s Good Morning Britain: “It will be up to each and every individual MP to make a decision of what they want to do when the time comes.”
Lib Dem deputy leader Daisy Coooper said: “The buck stops at the very top of government – if Rishi Sunak really wanted to govern with integrity he shouldn’t be running scared of this vote.”
It is not clear whether there ultimately will be a vote on the conclusions of the report, which could go through on the nod unless there are objections from Mr Johnson’s supporters.
The former prime minister was urging his allies not to oppose it, though loyalist Bill Cash said he would vote against it. Scores of Tories are expected to abstain, with cabinet minister Michael Goves saying the 90-day suspension was “not merited”.
Tory MPs will be given a free vote, but allies of Mr Johnson warned they could face battles with their local parties to remain as candidates at the next election if they back the motion.
The motion on the privileges committee’s findings comes as Scotland Yard is “considering” the footage from a December 2020 Christmas gathering at Conservative Party headquarters.
The Sunday Mirror obtained a video appearing to show Conservative staff dancing and joking about Covid rules. Both former London mayoral candidate Shaun Bailey and Tory aide Ben Mallet – who were handed a peerage and an OBE, respectively – attended the gathering.
Sir Keir said he does not believe either should receive an honour, and argued that “most” of the public would think it “simply inappropriate” for them to be recognised.
The Labour leader also ruled out putting forward a resignation honours list if he becomes prime minister, saying the tradition was “very hard to justify”.
The opposition leader told BBC Radio 4’s Today programme: “I think it is easier to be clean about this and say no, I wouldn’t do it. Tony Blair didn’t do it and I wouldn’t do it.”
Join our commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies