The shock outcome of the June 23 referendum has led to massive political upheaval, with warnings about the country's economic future and fears about the very unity of the United Kingdom.
The maverick Johnson had been tipped as a favourite to succeed Cameron, who resigned after the vote saying he would leave it to his successor to begin formal talks with the EU on Britain's departure -- despite European leaders insisting on a quick divorce.
The frontrunner in the five-horse race is now interior minister Theresa May, who supported staying in the EU but insisted she would honour the referendum outcome and lead Britain out of the bloc.
Johnson made his announcement after fellow Brexit campaigner Michael Gove effectively torpedoed his chances by announcing his own surprise bid for the top job, sharply criticising his mop-haired ex-ally.
'Greatest constitutional crisis'
The power struggle brought comparisons to Shakespeare tragedies, with one MP likening Gove's actions to those of a murderous Macbeth.
Senior Conservative Michael Heseltine said Johnson -- author of a book on Britain's wartime leader Winston Churchill -- was "like a general, that led his army to the sound of guns, and at the sight of the battlefield abandoned the field."
He accused Johnson of generating "the greatest constitutional crisis of modern times".
After an 11-minute speech trumpeting his achievements as London mayor and outlining his vision for Britain, Johnson left the punchline for the end.
"Having consulted colleagues and in view of the circumstances in parliament, I've concluded that person cannot be me," he told shocked supporters.
'Like a general, that led his army to the sound of guns, and at the sight of the battlefield abandoned the field.'
He also appeared to quote some of the words spoken by Brutus before he killed Julius Caesar in the Shakespeare play -- quickly interpreted by political commentators as a reference to Gove's actions.
Observers were left stunned by the dizzying events in the corridors of power, where opposition Labour leader Jeremy Corbyn is also clinging on to his job despite a mass revolt by his party's MPs and the resignation of top members of his shadow cabinet.
As the political drama played out, Bank of England governor Mark Carney warned about "heightened uncertainty" following the "Leave" campaign's victory.
He extended emergency liquidity loans for banks until September and hinted at possible interest rate cuts, sending the pound tumbling further against the euro.
Sterling was at 83.8 pence per euro at 1515 GMT, surpassing the previous low reached in March 2014. It also slid to $1.3234 but was still up from the 31-year low of $1.3121 it touched on Monday.
London's FTSE 100 has staged a strong recovery over the last 48 hours, closing 2.27 percent higher on Thursday.
"One uncomfortable truth is that there are limits to what the Bank of England can do," Carney said.
He said the Brexit vote could increase unemployment and warned there were also "risks of adverse spillovers to the global economy".
'Brexit means Brexit'
While not seen as a passionate supporter of the EU, interior minister Theresa May insisted "Brexit means Brexit".
"The campaign was fought, the vote was held, turnout was high and the public gave their verdict," she added.
May said she would not trigger the formal process for leaving the EU known as Article 50 until next year, despite pressure from other European countries.
Gove said he would "not be dictated to on the timetable of the manner of the negotiations" and would only begin negotiations when it was "right for Britain" if he is voted into power.
There are five candidates in the race to be Conservative leader, who will automatically become prime minister.
They will be whittled down to two by a series of ballots by Conservative MPs in the coming days before being put to a vote of grassroots party members.
The new leader will be announced on September 9.
Corbyn digs in
The outcome, after an often acrimonious campaign, triggered anger among those who wanted to remain in the 28-member EU. More than four million people have signed a petition calling for a second referendum.
The Labour party is also in turmoil over the vote, as lawmakers moved in to oust Corbyn, who has been accused of not campaigning hard enough to stay in the EU.
Although Labour lawmakers this week passed a vote of no confidence against him by 172 to 40, the veteran socialist has refused to go.
He insists he still has the support of party members and will fight any leadership challenge which he sees as a plot by centrist elements within Labour.