Labour is demanding investigations into fresh standards allegations against the Prime Minister and Commons Leader Jacob Rees-Mogg as sleaze claims continue to dog the Government.

The opposition party has said that new information from American entrepreneur Jennifer Arcuri about her relationship with Boris Johnson while he was mayor of London should be investigated by the Independent Office for Police Conduct (IOPC).

Mr Johnson avoided a criminal investigation earlier this year into his conduct with the businesswoman after the police watchdog found no evidence he had influenced the payment of thousands of pounds of public money to Ms Arcuri or secured her participation in foreign trade trips he led.

But after the Observer published Ms Arcuri’s diary notes from the time of their alleged dealings, deputy Labour leader Angela Rayner said the IOPC should “look again” at its decision to rule out a formal investigation.

According to the newspaper, one handwritten entry recalls that Mr Johnson asked how he could be the “throttle” in her career while he was in City Hall.

As well as having business links, Ms Arcuri has previously claimed that she and Mr Johnson had a four-year romantic relationship when he was mayor.

Ms Rayner has written to the Greater London Authority’s monitoring officer, Emma Strain, to request that she refer Ms Arcuri’s remarks to the IOPC.

In her letter, she said the reports were “deeply worrying” and “emblematic” of Mr Johnson’s approach to political leadership, which she claimed had “no regard for decency or public interest, only self-interest”.

Labour also wants Mr Rees-Mogg investigated by Commons standards commissioner Kathryn Stone over claims in the Mail On Sunday that the prominent Conservative MP failed to declare director’s loans from his company Saliston Limited between 2018 and 2020

Shadow Commons leader Thangam Debbonaire said: “This would appear to be yet another egregious breach of the rules.

“A Cabinet minister failing to declare millions of pounds of additional income is unacceptable.”

The allegations come after the Department for Transport (DfT) hit back at claims in the Sunday Times that Grant Shapps, a keen pilot, is using a lobbying body to protect airfields from development.

The Transport Secretary – who is said to own a £100,000 aeroplane – “set-up and diverted public money” to a new team within the Civil Aviation Authority which is designed to lobby against planning developments, including housing projects, that infringe on airstrips, according to the reports.

But DfT officials said the Airfield Advisory Team was not a lobbying body and instead provided “support to general aviation on a range of matters affecting their operations”.

The Tories have been rocked in recent days after opinion poll results suggested claims of sleaze have damaged their standing with voters, with as many as four surveys in the past five days suggesting Mr Johnson’s governing party has lost its lead over Labour.

One poll by Savanta ComRes poll put Labour six points ahead, with the Prime Minister’s personal ratings also plummeting.

But Labour too have faced questions over second jobs and consultancy, with party leader Sir Keir Starmer said to have previously advised the Government of Gibraltar and taken on external work.

The Sunday Times reported that Sir Keir has received more than £100,000 for providing legal advice since becoming an MP in 2015.

Ms Rayner told the BBC her party wanted to ban MPs from being paid for consultancy and from holding directorships.

The findings come after the Government attempted to rip up the current Commons standards system to delay former Tory cabinet minister Owen Paterson’s suspension for breaking lobbying rules, and revelations former attorney general Sir Geoffrey Cox voted by proxy while offering legal services in the Caribbean.

Mr Paterson opted to resign as MP for North Shropshire after 24 years after ministers U-turned on their standards reforms when opposition parties made clear they would not support them.

The messy handling of the affair has since thrust how much time and money MPs raise from second jobs back into the spotlight, along with scrutiny of second home arrangements.