The less high-profile, Mr Cain - a former tabloid journalist who once dressed as a chicken to goad Mr Johnson's predecessor David Cameron - had been offered the post of chief of staff.
It is in this spirit, that Johnson's partner and former Conservative Party head of communications, Carrie Symonds, is said to be steering the PM away from the former core of the Vote Leave campaign and towards the fledgling, more liberal alliance forming in No. 10.
But Mr Cain, the outgoing director of communications, remained for a farewell reception in the press office.
Boris Johnson's right hand man Dominic Cummings has left Downing Street after a power struggle that has rocked the Prime Minister's administration.
"I would suggest there are three words that need to become the watchwords in Downing Street - they are respect, integrity and trust", Jenkin told the BBC.
The online advertising blitz highlighting the idea of a potential influx of migrants from Turkey if Britain remained in the European Union - even though there was no immediate prospect of the nation joining the bloc - was also Mr Cummings' responsibility.
Mr Cummings had originally said he would leave his position at the heart of No 10 when Brexit is done at year-end, but was seen leaving Downing Street on Friday afternoon carrying a cardboard moving box.
Senior Tory aides were embroiled in a briefing war after it was revealed that the Prime Minister plans to promote communications chief Lee Cain to the powerful role of chief-of-staff.
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A series of Conservative MPs have welcomed the news as a chance for Boris Johnson to get a fresh start.
U.K. Transport Secretary Grant Shapps downplayed the departure of Cummings.
In a blog post in January, Mr Cummings revealed he planned to leave his role by the end of the year, saying he hoped to make himself "largely redundant" by then.
The resignation of Downing Street director of communications, Lee Cain on Wednesday was widely viewed as the outcome of an internal struggle within the prime minister's inner circle.
He courted damaging controversy earlier this year after making a cross-country journey during the coronavirus lockdown which appeared to breach strict regulations he had helped to design.
But No. 10 said Mr Cummings would continue to work for the PM until mid-December, although it was unclear in what capacity and whether he would return to the building. "The prime minister needs to put it to good use - and if he does, this could turn out to be a really good week".
But he was also credited with the extraordinary success of the Conservatives' 2019 election campaign, likely coming up with the campaign slogan "Get Brexit Done," which helped the party win a giant majority in Parliament and deal a decisive blow to the opposition Labour Party in deprived former industrial heartland seats that traditionally voted Labour but also leaned strongly toward Brexit.
It added that Johnson is said to want to "clear the air and move on".
Cummings is the second key adviser to Johnson to go in the space of a day, after tensions blew up over the way the prime minister's inner circle operates.