SNP Westminster leader Ian Blackford has called on the head of the civil service to investigate the "rule-breaking and the Tory Government's cover-up" of Dominic Cummings' lockdown journey to Durham.
The Prime Minister's top aide has come under fire after it emerged he had driven 250 miles despite the guidelines on travelling - and showing symptoms of coronavirus.
In the letter to Sir Mark Sedwill and Boris Johnson, Mr Blackford highlights the "matter of serious public concern" with several questions for the PM including when he found out about the trip and what role the UK Goverment played in "keeping the public in the dark for eight weeks".
He also continued his calls for Mr Cummings to resign over the fiasco, stating his position as "completely untenable".
Mr Blackford said: "I have written to Sir Mark Sedwill seeking an immediate investigation into the rule-breaking and the Tory Government's cover-up - and to call for Dominic Cummings to resign or be sacked.
"Boris Johnson must answer serious questions about his role in this incident and the cover-up - including when he found out, when he heard about the police action, why Mr Cummings wasn't sacked immediately, and why he kept the public in the dark for eight weeks until a newspaper broke the story.
"Dominic Cummings' position is completely untenable.
"This is a matter of leadership and judgment for the Prime Minister who must prevent lasting damage to his Government and his own reputation.
"Millions of us have made huge sacrifices over the months to obey the rules, while Boris Johnson's most senior adviser was breaking them.
"There cannot be one rule for the Tory Government and another for the rest of us."
Last month Scotland's then chief medical officer was forced to resign after being criticised for not adhering to social distancing advice.
Dr Catherine Calderwood apologised and was backed by First Minister Nicola Sturgeon to remain in the role, despite twice visiting her second home in Fife.
Photos of her and her family near a coastal retreat in Earlsferry - a drive of more than an hour from her main Edinburgh residence - were published in a national newspaper.
Mr Blackford also referred to Dr Calderwood's resignation and the reaction of the Scottish Conservatives in his reasoning for the letter addressing Mr Cummings' actions.
He added: "The excuses are not credible.
"There was absolutely nothing in the list of reasons under the law for leaving the house that allowed someone to travel the length of the country to stay with their parents, particularly not someone who was known to have the virus.
"The Tories vociferously demanded the resignation of Catherine Calderwood that same weekend.
"As Scottish Tory leader Jackson Carlaw said at the time 'There cannot be one rule for bosses and another for everyone else'.
"People are understandably questioning Boris Johnson's judgment. He must show Dominic Cummings the door and answer for his own role.
"Questions over the Tory cover up will only grow unless credible answers are provided - or until Mr Cummings is removed from his post."
Speaking after a UK Government briefing at which Transport Secretary Grant Shapps said Mr Cummings had the Prime Minister's "full support", Mr Blackford told the BBC: "He ought to have resigned by now, but it's quite clear after that performance today by the Transport Secretary that there is no real defence and that Dominic Cummings should now be sacked by the Prime Minister."
He said the Prime Minister should have been answering questions at the briefing, adding that Mr Cummings has "undermined the public messaging that the UK Government has sought to deliver".