In his report, external, Commissioner for Standards Martin Jelley said Baroness D’Souza’s actions “may harm the House by eroding public trust in parliamentarians and in institutions which exist to serve the public interest”.

In the letter, Baroness D’Souza complained the offences would result in 12 points on her driving licence, which meant she would lose it and might have to “give up attending Parliament”.

“I live deep in the countryside with no local bus services and unsuitable train schedules,” she added.

The peer had asked Sir Mark if losing her licence was “a fair response for exceeding the speed limit while we are all still learning what a 20-mile speed actually feels like?”

“Who can say if my speedometer or your radar is entirely accurate in recording 21 miles instead of 20,” she added in her letter, which was sent on House of Lords headed paper.

Baroness D’Souza, a crossbench peer who does not belong to a party, was eventually disqualified from driving temporarily on 16 July. She has only spoken in the House of Lords once since then and, voted twice.

In the letter, she acknowledged that Sir Mark, the UK’s most senior police officer who also leads on Britain’s counter-terrorism efforts, had “much other business to deal with”.

“I apologise for bothering your office with such a trivial matter,” she added.

The Met Police passed the letter to the House of Lords’ commissioner for standards who recommended an eight-week suspension, citing the aggravating factor that the intervention was for personal benefit.

Baroness D’Souza, who was the Lords’ speaker between 2011 and 2016, denied she had been attempting to influence the police investigation, but instead find “any mitigating factors” that might keep any driving ban to a minimum.

She told investigators she used Lords stationery because she had previously met Sir Mark “in the context” of her parliamentary role.

Baroness D’Souza accepted that her letter to the Met Police chief was “inappropriate” and said she “deeply regretted” the decision to send it.

She appealed against the proposed eight-week Lords ban, claiming it was “unduly severe” compared with shorter suspensions for bullying or misuse of facilities.

Her appeal was rejected by the committee.

The report will now go before the House for approval. If agreed, the suspension will take effect immediately.