Tory MPs have been warned that they will become the focal point of Labour campaign material and advertising if they do not vote for an investigation into whether Boris Johnson misled Parliament over partygate claims.

Labour has tabled a motion calling for the Prime Minister to be referred to the Commons Privileges Committee over allegations he was untruthful when he assured the Commons that coronavirus regulations were followed in Downing Street during the pandemic.

Mr Johnson has since been fined by Metropolitan Police officers for his part in a Cabinet Room birthday bash in June 2020, with more fixed-penalty notices a possibility as the inquiry into potential Covid-19 regulation breaches at the heart of Government continues.

Sir Keir Starmer’s party is calling on Conservative MPs to back its call for a Privileges Committee probe during a vote on Thursday, threatening to make those who support Mr Johnson the subject of campaign advertising.

Without Tory votes, the motion, which was published on Wednesday, is destined to fail, despite being backed by figures from six other opposition parties.

A spokesman for the Labour leader said that those voting down the motion would be considered to not “believe that honesty and integrity matters in public life”.

Meanwhile, Lib Dem MP Helen Morgan, who replaced former Conservative MP Owen Paterson in the North Shropshire seat after he resigned over a lobbying scandal, has called on 50 Tories in “Blue Wall” constituencies to rebel in Thursday’s vote – if they are whipped to oppose the investigation.

Tory MPs are expected to be ordered to vote against the Labour-led cross-party motion on Thursday, but it appears no final decision has yet been made by the whips.

Speaking to reporters after Prime Minister’s Questions, Sir Keir’s spokesman said: “This is a clear example where Conservative MPs should vote with their conscience and vote for this to be investigated.

“We know the facts, the public know the facts.

“Denying the reference to the Privileges Committee isn’t going to sway the public that there wasn’t widespread rule-breaking in No 10.

“It is simply going to confirm the impression that Conservative MPs believe there is one rule for the Government and another rule for everyone else.”

He added: “We certainly think that anyone who doesn’t support our motion is sending a message that they don’t believe that honesty and integrity matters in public life.

“And we will be absolutely looking to ensure that there is a price for Conservative MPs – in the way in which we campaign, in the advertising we will be putting out in individual constituencies – highlighting the fact that individual Tory MPs decided not to support an investigation into these matters.”

No 10 said it was not commenting on the motion until it had more time to study its wording.

In a letter to the 50 Tory MPs, Ms Morgan urged them to pick “decency and integrity” over “sleaze and scandal”, claiming that “British democracy is being dragged through the mud”.

She wrote: “This week marks five months since I won the North Shropshire by-election in the wake of a Conservative Party drowning in sleaze and scandal. It is sad to see your party has learnt nothing since then.

“Tomorrow you have the chance to learn from your mistakes. The public won’t stomach more cover-ups and lies, just ask the people of North Shropshire.”

She added: “The power is in your hands. You have the numbers to stop this stitch-up. So what will it be: sleaze and scandal? Or decency and integrity?”

Labour’s intention is that, should the Commons back the motion’s terms on Thursday, an investigation by MPs on the Privileges Committee would be delayed until the police inquiry has been completed.

The Prime Minister is due to be in India when the vote takes place.