The Prime Minister has been urged to “show some backbone” and order an investigation into claims Suella Braverman asked civil servants to help her secure a special arrangement after being caught speeding.

Deputy Labour leader Angela Rayner has written to Rishi Sunak setting out a series of questions any inquiry into the allegations should seek to answer.

The Home Secretary is alleged to have asked Home Office officials to help organise a one-to-one driving awareness course as she sought to avoid incurring points on her licence.

Officials refused the request so Mrs Braverman allegedly turned to a political aide to assist her in attempting to arrange an alternative to having to attend a course with other motorists.

Labour said Mrs Braverman may have breached the ministerial code if the reports, which first appeared in The Sunday Times, are correct and is calling for Mr Sunak’s independent adviser on ministerial interests, Sir Laurie Magnus, to investigate.

Mr Sunak refused to back Mrs Braverman when asked for his opinion at a press conference in Hiroshima, Japan, where he had been meeting with G7 leaders.

But No 10 has since said he does have full confidence in his Home Secretary, who is likely to face queries about the reports when she comes before MPs at Home Office questions in the Commons on Monday.

In her letter to Mr Sunak, Labour’s Ms Rayner said the Prime Minister should order an investigation “without delay”.

She added: “Members of the Cabinet are subject to the same laws as the rest of us, and any attempt to direct civil servants to obtain special treatment in this matter would clearly amount to an unacceptable abuse of power and privilege by the Home Secretary.”

Ms Rayner, in a separate statement, said: “The Prime Minister must show some backbone and order his ethics adviser to investigate the Home Secretary to get to the bottom of this episode without further delay.

“The public have a right to know whether the minister responsible for law and order sought to abuse her position in an attempt to gain preferential treatment to avoid a speeding fine.

“This Conservative Cabinet appear to think they are above the laws that govern the rest of us.”

Mrs Braverman was appointed to her Home Office role by Mr Sunak in October only six days after she resigned as home secretary during Liz Truss’ premiership for sharing a sensitive document with a Tory backbencher from a personal email without permission.

In his first speech after entering Downing Street, Mr Sunak vowed to lead an administration with “integrity, professionalism and accountability at every level”.

Ms Rayner continued: “Rishi Sunak was too weak to deal with Suella Braverman the last time she broke the ministerial code, and his reluctance to order an investigation right away speaks volumes on how seriously he takes his promise to bring integrity to Government.”

The senior Labour MP’s letter says Sir Laurie should probe whether Mrs Braverman asked civil servants to help her enlist in a private driving course.

She suggested that to have done so could breach paragraph 1.3 of the ministerial code which states that ministers must uphold the political impartiality of the Civil Service and not ask civil servants to act in any way which would conflict with the Civil Service Code.

The code by which civil servants must abide states that public servants must not “misuse [their] official position […] to further [their] private interests or those of others”.

Ms Rayner also asks whether Mr Sunak knew about the alleged request to civil servants to help her arrange a special course and whether Mrs Braverman informed the Cabinet Office and Home Office permanent secretaries.

A source close to Mrs Braverman told PA news agency that she notified the Cabinet Office after being handed the speeding ticket, having reportedly been caught driving too fast on a road outside of London last summer.

A spokesman for the Home Secretary said she regrets speeding and has since accepted the points and paid the fine.

Separately, the Liberal Democrats are calling on Mr Sunak to make a statement in Parliament about the claims surrounding his Cabinet minister.

The party’s chief whip, Wendy Chamberlain, said: “Rishi Sunak is so weak he can’t even make sure his own ministers maintain the very basic level of integrity.

“The least he can do is come to Parliament and explain this farce. After yet another day of Conservative sleaze and scandal, we need to see the Prime Minister take some responsibility.”