A senior peer has written to the Metropolitan Police Commissioner and Director of Public Prosecutions calling for a probe into claims the Tories offered peerages to senior Brexit Party figures in a bid to get them to stand aside in the General Election.

Lord Falconer said the “exceptionally serious allegations” should be investigated as a matter of urgency, and must be looked at by police in order to maintain public confidence in the integrity of the election.

The Labour former lord chancellor’s letter to Dame Cressida Dick and Max Hill QC refers to Nigel Farage’s claim that he and eight other senior figures within the Brexit Party were offered peerages.

Mr Farage has claimed he had repeatedly been offered a seat in the House of Lords in an attempt to persuade him to “go quietly”.

He said that when that failed, people working “deep inside Number 10” had tried to bypass him, going directly to senior Brexit Party figures and suggesting eight of them could be made peers if they could persuade him to withdraw more of his candidates.

Lord Falconer wrote: “I wish to raise with you as a matter of urgency a number of recent reports in which senior figures in the Brexit Party have alleged that some of their candidates had been approached by the Conservative Party in an effort to persuade them to withdraw their candidacies from the upcoming General Election.”

He added: “I believe these allegations raise serious questions about the integrity of the upcoming General Election, and in particular whether senior individuals at CCHQ or No. 10 have breached two sections of the Representation of the People Act 1983.”

He then cites the parts of the Act which refers to “bribery” and “corruptly”, inducing or procuring someone to withdraw from being a candidate at an election.

Lord Falconer said that as breaches of the 1983 Act may have taken place, he is “formally requesting that the Director of Public Prosecutions do institute the necessary investigations and commence such prosecutions as he sees fit”.

The Prime Minister acknowledged that there may have been “conversations” between senior Tories and people in the Brexit Party, but flatly denied there had been any offers of peerages, saying that was “just not the way we operate”.

Lord Falconer said: “These are exceptionally serious allegations which the DPP must, in accordance with his statutory duty, fully investigate as a matter of urgency.

“In addition, in order to maintain public confidence in the integrity of our electoral processes and this election, it is crucial that the Metropolitan Police also examine these accusations.”

The row came amid growing pressure on Mr Farage in the run-up to the close of nominations on Thursday to stand down Brexit Party candidates in all but a few dozen constituencies to avoid splitting the pro-Leave vote.

The Brexit Party leader had already said they would not contest the 317 seats which the Conservatives had won in the 2017 election.

However, senior Tories warned that he was risking the chance of a pro-Brexit majority in the next parliament by continuing to run candidates in key marginals which the Conservatives are aiming to take from Labour.

Suspicions that individual Brexit Party candidates were coming under pressure to stand aside were heightened after the prospective candidate for Dudley North announced he would not be running.

Rupert Lowe, a Brexit Party MEP and former chairman of Southampton FC, revealed his decision as nominations were closing – meaning it was too late for the party to put forward an alternative.

In a video posted on Twitter, Mr Farage said there had been “a concerted attempt from people who work deep inside Number 10 Downing Street” to ensure the Brexit Party did not field candidates in seats the Tories were targeting.

Lord Falconer’s letter includes a mention of Ann Widdecombe, the former Tory MP now standing for the Brexit Party in Plymouth Sutton and Devonport.

Ms Widdecombe said she was offered a role in the Brexit negotiations if she was prepared to stand aside.

She declined to say who she had spoken to, although she said it was not Mr Johnson or his senior advisers Dominic Cummings and Sir Edward Lister.

A tweet from Mr Farage, which mentioned Sir Edward, said: “Even Boris Johnson’s Chief Strategic Adviser Sir Edward Lister is calling our candidates and offering them jobs if they withdraw. The system is corrupt and broken.”