The Prime Minister’s spokesperson said that holding another vote was “not remotely on the cards”. The clarification comes amid a petition calling for a re-run in the event of a close result and following speculation that the government may go to the country again once the terms of Britain’s new relationship have been agreed.
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Mr Cameron chaired the first Cabinet meeting since the Brexit vote at midday on Monday, where ministers confirmed plans for a special government unit to draw up options for Britain’s renegotiation with the EU.
However, formal negotiations cannot start until Britain activates Article 50 – initiating the formal two-year procedure for withdrawing from the EU. Mr Cameron has said this will be a task for the next Prime Minister, who will not be in place until a Conservative leadership election has concluded by October.
And also on Monday, the head of the Brexit campaign said it was important to delay the formal process of leaving the EU because people need to "go away on holiday".
Vote Leave chief executive Matthew Elliott welcomed Mr Cameron's decision to delay the "divorce" for several months, despite pressure from Brussels for a rapid departure.
"I don't think we need to rush this process," he told US TV channel CNBC.
"During the campaign there was talk about triggering Article 50 and its process of leaving the EU right away, literally on Friday morning, and I think quite rightly the PM has paused on that which allows the dust to settle, allows people to go away on holiday, have some informal discussions about it, and then think about it come September/October time."
He said Vote Leave had "done lots of detailed planning" for Brexit and suggested Michael Gove was "probably the man to lead the negotiations" - but dismissed the idea of any formal role for Ukip leader Nigel Farage.
Economic turbulence would "settle very quickly", he predicted.
Mr Cameron will face MPs in the House of Commons later this afternoon, and make his first statements on the Brexit vote and its aftermath since he announced his resignation on Friday.
Asked about the possibility of a second vote, the Prime Minister’s spokesperson said: “That’s not remotely on the cards. There was a decisive result [in the EU referendum]. The focus of the Cabinet discussion was how we get on and deliver that.”
Earlier, sterling slipped to a new 31-year low against the dollar as George Osborne sought to calm volatile markets.
The pound had dipped to $1.3231 on Thursday night - the lowest since 1985 - as the referendum result came into focus and traders sold sterling. But it recovered slightly over the following 24 hours.
David Cameron's premiership - in pictures
Show all 15
David Cameron's premiership - in pictures
1/15
Britain's Queen Elizabeth II greeting David Cameron at Buckingham Palace for an audience to invite him to be the next Prime Minister on 11 May 2010
PA
2/15
Prime Minister David Cameron and his wife Samantha wave from the steps of Number 10 Downing Street on 11 May 2010
Getty Images
3/15
On 12 May 2010 Prime Minister David Cameron said in a press conference with Lib Dem leader Nick Clegg, who was then deputy PM, they plan to "take Britain in a historic new direction" and Conservative-led coalition government would be united and provide "strong and stable" leadership
Rex
4/15
A decade ago, David Cameron visited the Arctic to witness the effects of climate change. However since coming to power in 2010, his government has gradually dropped down a succession of green policies
5/15
Prime Minister David cameron told the then New York mayor Michael Bloomberg, the Queen had “purred down the line” after he told her Scotland had voted against independence in September 2014. He was forced to apologise for breaking constitutional convention
Getty Images
6/15
Britain's Prime Minister David Cameron greeted soldiers working on flood relief in York city centre after the river Ouse burst its banks, in northern England in December 2015
REUTERS
7/15
Claims that David Cameron performed an obscene act with a dead pig and smoked cannabis during his studies at Oxford University spread around the world in September 2015. The extraordinary allegations were made in an unauthorised biography of the Prime Minister written by Lord Ashcroft
David Hartley/REX Shutterstock
8/15
In 2016, Mr Cameron was caught up in a worldwide scandal dubbed the “Panama papers”
Reuters
9/15
Prime minister David Cameron and his wife Samantha with seven week old Regan as they meet her parents, first time home buyers Robert Arron and Kelly Jeffers at the Heritage Brook housing development in Chorley, Lancashire. David Cameron has joked that he wants "another baby" and said that he feels a "bit broody" every time he sees a newborn on the campaign trail
10/15
Prime Minister David Cameron was criticised for branding refugees in the Calais ‘jungle’ camp as a “bunch of migrants” in January 2016 after thousands of refugees died in their attempt to cross the Mediterranean in 2015
Sky News
11/15
Britain's Prime Minister David Cameron speaks with European Commission President Jean-Claude Juncker during an EU summit meeting on 17 March 2016 at the European Union council in Brussels. Cameron was in Brussels to renegotiate deal of UK membership with other European leaders. The deal, sealed after hours of haggling at a marathon summit, paved the way for a referendum on whether Britain will stay in the EU
AFP/Getty Images
12/15
President Barack Obama shakes hands with British Prime Minister David Cameron at a meeting at 10 Downing Street in London on 22 April 2016. The President and his wife visited 10 Downing Street where he joined press conference with British Prime Minister David Cameron and made his case for the UK to remain inside the European Union
Getty Images
13/15
After David returned from Brussels claiming victory in his renegotiation with European leaders, Boris Johnson announced that he will not support the Remain campaign. The prime minister said publicly he was "disappointed but Boris remains a friend"
PA
14/15
Prime Minister David Cameron makes a joint appearance with Mayor of London Sadiq Khan as they launch the Britain Stronger in Europe guarantee card at Roehampton University on 20 May 2016 in London. The 'guarantee card' lists five pledges should Britain remain in the EU, including the protection of workers' rights, full access to the single market and stability for Britain
15/15
Britain's Prime Minister David Cameron speaks outside 10 Downing Street on 24 June 2016. Cameron announced his resignation after Britain voted to leave the European Union after a bitterly divisive referendum campaign
AP
1/15
Britain's Queen Elizabeth II greeting David Cameron at Buckingham Palace for an audience to invite him to be the next Prime Minister on 11 May 2010
PA
2/15
Prime Minister David Cameron and his wife Samantha wave from the steps of Number 10 Downing Street on 11 May 2010
Getty Images
3/15
On 12 May 2010 Prime Minister David Cameron said in a press conference with Lib Dem leader Nick Clegg, who was then deputy PM, they plan to "take Britain in a historic new direction" and Conservative-led coalition government would be united and provide "strong and stable" leadership
Rex
4/15
A decade ago, David Cameron visited the Arctic to witness the effects of climate change. However since coming to power in 2010, his government has gradually dropped down a succession of green policies
5/15
Prime Minister David cameron told the then New York mayor Michael Bloomberg, the Queen had “purred down the line” after he told her Scotland had voted against independence in September 2014. He was forced to apologise for breaking constitutional convention
Getty Images
6/15
Britain's Prime Minister David Cameron greeted soldiers working on flood relief in York city centre after the river Ouse burst its banks, in northern England in December 2015
REUTERS
7/15
Claims that David Cameron performed an obscene act with a dead pig and smoked cannabis during his studies at Oxford University spread around the world in September 2015. The extraordinary allegations were made in an unauthorised biography of the Prime Minister written by Lord Ashcroft
David Hartley/REX Shutterstock
8/15
In 2016, Mr Cameron was caught up in a worldwide scandal dubbed the “Panama papers”
Reuters
9/15
Prime minister David Cameron and his wife Samantha with seven week old Regan as they meet her parents, first time home buyers Robert Arron and Kelly Jeffers at the Heritage Brook housing development in Chorley, Lancashire. David Cameron has joked that he wants "another baby" and said that he feels a "bit broody" every time he sees a newborn on the campaign trail
10/15
Prime Minister David Cameron was criticised for branding refugees in the Calais ‘jungle’ camp as a “bunch of migrants” in January 2016 after thousands of refugees died in their attempt to cross the Mediterranean in 2015
Sky News
11/15
Britain's Prime Minister David Cameron speaks with European Commission President Jean-Claude Juncker during an EU summit meeting on 17 March 2016 at the European Union council in Brussels. Cameron was in Brussels to renegotiate deal of UK membership with other European leaders. The deal, sealed after hours of haggling at a marathon summit, paved the way for a referendum on whether Britain will stay in the EU
AFP/Getty Images
12/15
President Barack Obama shakes hands with British Prime Minister David Cameron at a meeting at 10 Downing Street in London on 22 April 2016. The President and his wife visited 10 Downing Street where he joined press conference with British Prime Minister David Cameron and made his case for the UK to remain inside the European Union
Getty Images
13/15
After David returned from Brussels claiming victory in his renegotiation with European leaders, Boris Johnson announced that he will not support the Remain campaign. The prime minister said publicly he was "disappointed but Boris remains a friend"
PA
14/15
Prime Minister David Cameron makes a joint appearance with Mayor of London Sadiq Khan as they launch the Britain Stronger in Europe guarantee card at Roehampton University on 20 May 2016 in London. The 'guarantee card' lists five pledges should Britain remain in the EU, including the protection of workers' rights, full access to the single market and stability for Britain
15/15
Britain's Prime Minister David Cameron speaks outside 10 Downing Street on 24 June 2016. Cameron announced his resignation after Britain voted to leave the European Union after a bitterly divisive referendum campaign
AP
Yet in trading today the pound dipped below that level, as a statement by the Chancellor, George Osborne, highlighting the "strength" of the UK economy, failed to assuage concerns.
Boris Johnson, the figurehead of the Leave campaign and presumed Conservative leadership contender, said in his Daily Telegraph column this morning that "the pound remains higher than it was in 2013 and 2014". But he is believed to have been referring to the pound versus the euro, not the dollar.
In another sign of growing financial stress 10 year government bond yields - known as Gilts - fell below 1 per cent for the first time in history.
The Prime Minister has also condemned the rise in anti-migrant and racist incidents reported since the Brexit vote. The Downing Street spokesperson said that many MPs had received reports from their constituencies and communities of migrants being intimidated or “told they need to go home”.
“We are absolutely clear and we need to reassure communities across Britain…this government will not tolerate intolerance,” the spokesperson said.
Saying that Britain was a tolerant, inclusive nation, the spokesperson said: “Those views and that value of our nation existed long before we were members of the EU and we should hold fast to that value and stand up for that value in the days and weeks ahead
“There was a legal, fair and decisive referendum two years ago,” Mr Cameron's spokesperson said. “The reasons for Scotland being in the UK are as strong now as they were 18 months ago. What we all need to do is to focus on getting the best deal for Scotland and the UK in these negotiations and the last thing Scotland needs now is another divisive referendum.”
The stance will put the Government on a collision course with Holyrood and Nicola Sturgeon, who has said a second independence vote is "highly likely" following the UK's decision to Brexit.
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