The health minister James Bethell is under formal investigation for sponsoring the parliamentary pass of Gina Coladangelo, the aide Matt Hancock had a relationship with in breach of Covid rules.

The House of Lords standards commissioner said they were looking into Lord Bethell’s “use of facilities” – understood to relate to the pass he secured for Coladangelo that gave her unfettered access to parliamentarians and the Palace of Westminster estate.

Labour had called for an inquiry over the weekend, saying Bethell was Hancock’s “chum” and “dished her out a pass”, raising the prospect that there was “one rule for the Conservatives and their friends and another for everyone else”.

Anneliese Dodds, the Labour chair, demanded to know what help Coladangelo gave Bethell, given peers are only allowed to provide passes to carers, spouses and those who “genuinely and personally provide parliamentary secretarial or research assistance to the sponsoring member”.

In a letter defending his actions to the Lords commissioner, seen by the Guardian, Bethell said Coladangelo was unpaid and helped him with parliamentary research, drafted speeches and engaged with stakeholders.

He said Coladangelo’s pass was granted on 12 March 2020 under the name Gina Tress, her married name, but the rules in relation to how lords could sponsor passes were changed in November 2020, and he cancelled the pass the following month.

But a senior Labour peer and former cabinet minister, George Foulkes, queried why the help Coladangelo gave Bethell was not performed by one of the thousands of civil servants in the Department of Health and Social Care.

He said it was “unprecedented for a minister with the vast resources of DHSC” to need an unpaid assistant that did the work Bethell said Coladangelo had done.

“As a former minister I know these are the tasks which a private office and public affairs officials of a department are there for,” Lord Foulkes said. “It looks to me like a front for other activities, whether personal or political, which the commissioners need to investigate.”

The DHSC has been contacted for comment.

After Hancock stepped down last month, it also emerged Bethell and another health minister, Helen Whately, had used personal email addresses to conduct government business. The information commissioner is conducting a separate investigation into the issue.

Bethell, who oversaw the award of Covid contracts, admitted to the practice but denied any wrongdoing. He told the Lords last week: “I have read and signed the ministerial code and I seek to uphold it in everything I do.”