Morgan McSweeney, the prime minister’s former chief of staff, has been summoned before the foreign affairs select committee as the Peter Mandelson vetting row continued to undermine Keir Starmer’s premiership.

As MPs attempt to unravel the facts, McSweeney is to appear next Tuesday to respond to allegations that Downing Street put huge pressure on the civil service to approve his appointment as the UK’s ambassador to Washington.

It is highly unusual for Downing Street chiefs of staff to appear before Commons committees even after they have left post, and the session is likely to be an explosive one as MPs are given the rare opportunity to question one of the most powerful figures in recent Labour history.

Olly Robbins, the top Foreign Office official sacked by Starmer, told MPs on Tuesday that No 10 had created an “atmosphere of pressure” that made it impossible to deny clearance for Mandelson and had taken a “dismissive” attitude to vetting.

Emily Thornberry, the committee chair, asked whether it had been McSweeney, to which Robbins said it was mainly the prime minister’s private office, which is staffed by civil servants. But he added: “I think that the private office would only have been [putting on] this pressure themselves if they were under pressure.”

McSweeney quit his role in February over Mandelson’s appointment, saying he took “full responsibility” for advising the prime minister to appoint Mandelson, who had been a close ally and political mentor.

The senior No 10 adviser’s position had grown increasingly untenable as pressure on Starmer mounted over the scandal, which followed the release of emails underlining the extent of Mandelson’s relationship with the convicted child sex offender Jeffrey Epstein.

The Mandelson scandal dominated PMQs on Wednesday, with Starmer coming under fire from the Tory leader, Kemi Badenoch, and Lib Dem leader, Ed Davey, over the issue. He said that Robbins’ evidence “puts to bed all the allegations levelled at me” after claims he had misled parliament.

However, Starmer appeared to confirm that No 10 had tried to find an ambassadorial posting for his former director of communications. “Matthew Doyle worked for many years in public service for me as PM and other ministers. When people leave roles there are often conversations about other roles, but nothing came of this,” he said.

Cat Little, the permanent secretary at the Cabinet Office who has been at the heart of the row between the Foreign Office and her department, is due to appear before the committee on Thursday, and is expecting to set out a counterpoint to Robbins’ evidence earlier this week.

She obtained the summary document on Mandelson’s vetting at the end of March and several weeks later, after taking legal advice and making other checks, she informed the prime minister. Sources said she had found it difficult to get information from the Foreign Office.

The Guardian understands that Little appeared in private before parliament’s intelligence and security committee on Tuesday. The ISC is understood to be furious at the lack of key documents relating to Robbins’ decision to overturn the recommendation to deny Mandelson security clearance, and his failure to record notes of crucial meetings.