Rishi Sunak will speak to his independent ethics adviser regarding Suella Braverman’s speeding fine, Sky News understands.
The prime minister will consult his adviser upon returning to London from the G7 summit in Japan.
Ms Braverman, 43, had been caught speeding last summer and opted to attend a driving awareness course rather than accept a fine and points on her licence.
In a letter written to Mr Sunak, deputy Labour leader Angela Rayner demanded that he go one step further and launch an independent investigation – as he did over Nadhim Zawahi’s tax affairs – into the claims.
She said the prime minister must “show some backbone” and investigate the claims “without further delay”.
Ms Rayner also questioned whether the home secretary “encouraged or asked civil servants, officials or special advisers to breach the civil service code by supporting her to further her own private interests” and whether the prime minister himself “knew about the alleged attempts by the home secretary to involve her civil servants”.
“Rishi Sunak was too weak to deal with Suella Braverman the last time she broke the ministerial code, and his reluctance or order an investigation right away speaks volumes on how seriously he takes his promise to bring integrity to government,” she said.
A spokesman for the home secretary said Ms Braverman “accepts that she was speeding last summer and regrets doing so”.
“She took the three points and paid the fine last year,” they added.
But The Sunday Times reported that instead of signing up for an in-person course with other motorists, or completing one online that would show her name and face to other participants, Ms Braverman allegedly asked civil servants to arrange a private one-to-one course.
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When the civil servants refused, she sought help from a political aide, who requested the private course organiser provided a private session, or allowed her to use an alias or turn her camera off.
When the provider refused, Ms Braverman opted to take the three points on her licence, the paper reported.
Earlier on Sunday, Mr Sunak refused to back the home secretary when asked about the row at the end of the G7 meeting by a reporter.
“I don’t know the full details of what has happened nor have I spoken to the home secretary,” he said.
“I think you can see first-hand what I have been doing over the last day or so but I understand that she’s expressed regret for speeding, accepted the penalty and paid the fine.”
However, a No 10 spokeswoman later insisted he does “of course” have full confidence in her.
Speaking on the Sky News Sophy Ridge On Sunday programme, Environment Secretary Therese Coffey said it was “perfectly normal” if people are given points for speeding, but maintained that she was unaware of all the details referred to in the newspaper.
Meanwhile, the incident was called “shocking” by Shadow Home Secretary Yvette Cooper.
“We’ve had 13 years of the Tories trying to dodge the rules for themselves and their mates. Enough is enough.” said Ms Cooper.
Labour’s shadow health minister, Liz Kendall, reiterated calls for Mr Sunak to launch an investigation into whether Ms Braverman breached the standards of the ministerial code.