Correspondence exists confirming that Boris Johnson attempted in 2019 to secure a senior role for his then girlfriend, Carrie Johnson, at the Foreign Office, a source has said, amid growing calls for an inquiry.

The source, who worked with Johnson at the time, said Carrie Johnson – now the prime minister’s wife – had never progressed as far as formally applying for the role.

But they claimed that Johnson, then foreign secretary, had repeatedly pressed for her to be picked for the senior taxpayer-funded job, a fact reflected in internal documentation from the period that could be examined by an inquiry.

The prime minister’s spokesperson has previously said they were unable to comment on Johnson’s activities before he became prime minister, but that “others have made clear this story is untrue”.

A former Foreign Office minister, Alan Duncan, also said he was told in 2018 that Carrie Johnson was a rising star running communications in Conservative campaign headquarters (CCHQ) and was being lined up for a special adviser role in the department.

“For someone slightly unproven who knew nothing about foreign affairs to come straight out of CCHQ and into the Foreign Office was rather noticeable,” Duncan told the Guardian.

He said he had no idea of the nature of her relationship with Johnson and the suggestion about her rapid promotion had only been cursorily mentioned, though added: “Had it got closer to the goal, people who knew more would have revealed more and then the bubble would have burst.”

Duncan said the suggestion that Johnson had tried to get his girlfriend a £100,000-a-year taxpayer-funded job was the latest evidence of his “dripping ceiling theory”. He explained: “They put one bucket under one drip, another bucket under another drip – but at some point the whole ceiling will come falling down.”

The chair of the House of Commons standards committee, Chris Bryant, called on Tuesday for the “paper trail” surrounding the issue to be published. “It is manifestly corrupt to appoint your lover as a Spad,” he said in a tweet.

At the time, Johnson was still married to his second wife, Marina Wheeler.

Bryant was urged by the Liberal Democrats’ chief whip, Wendy Chamberlain, to investigate the allegations, given the government’s ethics adviser role remains unfilled after the resignation of Christopher Geidt last week.

After Geidt said the claims “could be ripe for investigation”, Chamberlain said there was a “significant risk that no such inquiry will follow” because No 10 has not committed to replacing Geidt while it reviews the role.

Chamberlain said: “If found to be true, these allegations would amount to a serious breach of standards in public life and bring not just the office of prime minister into disrepute, but parliament and our politics as a whole.”

Given the standards committee can only conduct general inquires and those referred to it by the standards commissioner, Bryant would have to launch an investigation into “ministerial attempts to appoint people of interest” and then call Johnson as a witness to formally examine the case.

Labour’s deputy leader, Angela Rayner, raised concerns over the alleged attempt by Johnson to make an “inappropriate appointment to his own office”, but called it “just another case of dishing out jobs to those close to him”.

She said the country could not “endure another five months with no accountability in Downing Street” and joked that “to this prime minister, ethics is a county east of London”.

The Conservative MP Jackie Doyle-Price told the Commons in response that the person picked to replace Geidt “would be taking a massive reputational risk in taking the job”, and urged colleagues not to break the law or sully standards. “It should be in our DNA to play by the rules of the game,” she said.

Michael Ellis, the Cabinet Office minister, defied calls to put a time limit on filling Geidt’s role. He said the appointment would be made after “proper diligence and attention” and should not be concluded “in haste”.

After the Mirror reported that Johnson discussed giving environmental roles to his wife in autumn 2020, No 10 said the prime minister did not recommend her for any appointments but would not “get into any conversations he may or may not have had”.

Carrie Johnson’s spokesperson has called the claims about her being offered a job in the Foreign Office “totally untrue”. On the subsequent claims about attempts to find her a job elsewhere, they said: “This is an old story, as untrue now as it was then.”