The former head of the civil service said one problem with the ministerial code is that any potential breach is treated as a “gotcha moment”.

Sir Gus O’Donnell, who was cabinet secretary between 2005 and 2011, declined to say whether Home Secretary Suella Braverman broke the code over her handling of a speeding offence.

But he rejected the assumption that ministers should automatically resign if a breach is identified.

Speaking at an Institute for Government (IfG) event on Tuesday, Sir Gus said: “One of the things that was wrong about the ministerial code (is) that people thought, journalists in particular, about this, ‘Aha, gotcha. You broke the ministerial code therefore you must resign’, which is not true.

“It shouldn’t be true. It should be, ‘You broke the ministerial code, it is actually a relatively minor offence, I am going to give you a yellow card and we’ll move on’.

Ms Braverman resigned as home secretary last October after breaking the ministerial code by sending an official document from her personal email account to a fellow MP.

She was reinstated to the post when Rishi Sunak became Prime Minister.

Sir Gus said: “I stress in talking about this: I have no knowledge whatsoever about the Suella Braverman case so I cannot be caught… I don’t know (if she broke the ministerial code).

“But I am glad we have a process that allows those things to be investigated. It is sensible the Prime Minister is using that process.

“I would personally like the independent investigation to have, overall, more power to take up, to start investigations.

“Hopefully we will get to the bottom of this and then the Prime Minister will make a decision as to what should be done.”

Mr Sunak is under growing pressure to launch an investigation into allegations Mrs Braverman breached the ministerial code in the aftermath of being caught speeding while she was attorney general.

Officials formally raised concerns over an alleged request by the Home Secretary for them to arrange a one-to-one speed awareness course for her, The Times reported.

Mrs Braverman admits speeding, paying a fine and taking penalty points on her driving licence but insists she has done “nothing untoward”.

Mr Sunak spoke to his independent adviser on ministers’ interests, Sir Laurie Magnus, and Mrs Braverman on Monday as he considered his response.

Also appearing at the IfG event, former cabinet minister George Eustice said he did not know the circumstances of Mrs Braverman’s case but echoed Sir Gus’s view on the way events are being perceived.

He said: “There is a tendency sometimes where we have these rules for them to be turned into a kind of gotcha kind of debate.

“The thing that always surprised me about our system is rarely do people get done for any serious wrongdoing. It is usually some minor technical crossing of the line that then gets blown out of proportion.

“It is a big weakness in our system that we have these distractions.”