Downing Street has rejected calls for a wider inquiry into ministerial bullying but indicated that lessons could be learned about the handling of complaints.

FDA general secretary Dave Penman had warned that misconduct by senior members of Government is more widespread than Prime Minister Rishi Sunak wants to admit as he called for a wider probe into ministerial behaviour.

Mr Penman, who made the call following Mr Raab’s resignation, complained of the “inadequacy of a process that relies solely on the Prime Minister of the day to enforce standards”.

“This demonstrates that Raab is not just one bad apple, and there is a wider problem with ministerial bullying than the Prime Minister wants to admit,” Mr Penman said.

Mr Raab’s “obviously reluctant tone and dismissal of the complaints” in his resignation demonstrate why he has been forced out of Cabinet, the union leader suggested.

“The Prime Minister may have been left with no choice today, but he still has serious questions to answer over what he knew when he appointed Raab as Deputy Prime Minister in October,” Mr Penman said.

“The sad reality is that if he had appointed him to any other government department, his behaviour would, in all likelihood, still be going unchecked.

Given the scale of complaints against Dominic Raab and the evidence we have produced of a wider problem, the Prime Minister must now launch an independent inquiry into ministerial bullying

“This demonstrates that Raab is not just one bad apple, and there is a wider problem with ministerial bullying than the Prime Minister wants to admit.

But the Prime Minister’s official spokesman said an independent inquiry into ministerial bullying was not being considered.

While a broader review is not being considered, he confirmed that Mr Sunak had asked the Cabinet Office to look at how Government “can better learn to handle some of the issues that this report has raised, in terms of how concerns about working practices are raised in a timely manner and how they are dealt with”.

“I think that is in the interest of both civil servants and ministers.”

In his letter to Dominic Raab, Mr Sunak told his former deputy: “It is clear that there have been shortcomings in the historic process that have negatively affected everyone involved. We should learn from this how to better handle such matters in future.”