Boris Johnson has declared "Project Fear is over" after Chancellor George Osborne said an emergency post-Brexit budget was unlikely to happen until a new prime minister is in place in the autumn.

The leading Leave campaigner welcomed the early morning statement by Mr Osborne intended to calm the markets that the UK economy was "about as strong as it could be" to confront the challenge of separating from the EU.

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"It is clear now that Project Fear is over, there is not going to be an emergency budget, people's pensions are safe, the pound is stable, the markets are stable, I think that's all very good," he told reporters as he left his London home.

In his statement, Mr Osborne said he had held talks over the weekend with Bank of England Governor Mark Carney as well as fellow finance ministers and international economic organisations and that "further well-thought through contingency plans" were in place if needed.

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"It will not be plain sailing in the days ahead. But let me be clear - you should not underestimate our resolve," he said.

"We were prepared for the unexpected and we are equipped for whatever happens. And we are determined that, unlike eight years ago, our financial system will help our country deal with any shocks and dampen them, not contribute to those shocks or make them worse."

The assurances did not stop fresh warning from business about the likely consequences of last week's momentous vote to withdraw from the EU.

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Estate agent Foxtons issued a profit warning and said that the upturn it had expected in the second half of the year is "now unlikely to materialise", adding that annual earnings will be "significantly lower" than in 2015.

The budget airline easyJet also pointed to a host of events that will see it take a £28 million hit following two months of turbulence, adding that Brexit would also have a negative impact on the airline.

Meanwhile, Mr Johnson, the overwhelming favourite to succeed David Cameron after the Prime Minister announced his decision to quit, sought to reassure EU nationals living in the UK that their status would not be affected by the referendum vote.

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"It is absolutely clear that people from other European countries who are living here have their rights protected," he said.

"All that people want to see is a system that is fair, impartial and humane to all people who come here from around the world.

"People from the UK living in the rest of the EU will also have their rights completely protected."

Mr Cameron has been chairing an emergency Cabinet meeting, while US secretary of state John Kerry was visiting London and Brussels for talks on the fallout from the vote.

Meanwhile, Labour leader Jeremy Corbyn was insisting he will not stand down in the face of a rebellion which saw 11 members of the shadow cabinet quit over the weekend following the sacking of Hilary Benn as shadow foreign secretary.

Mr Osborne said that Article 50 of the Lisbon Treaty, which sets in train the two-year process of negotiating withdrawal from the EU, should not be invoked until a new prime minister has set out "a clear view about what new arrangements we are seeking with our European partners", effectively delaying talks until October at the earliest.

He made clear he expects to remain as Chancellor during that time, but gave no indication of whether he will run as a candidate to succeed Mr Cameron, saying that he would address questions about his role in the future of the Conservative Party in the coming days.

Despite accusations by Brexit supporters of scaremongering during the referendum campaign, Mr Osborne insisted he was not backing away from the warnings that there could be a £36 billion black hole in the public finances by 2030.

He said that volatility in the markets, which saw the pound fall to 30-year lows in the immediate aftermath of the referendum on Friday, was "likely to continue".

"It is already evident that, as a result of Thursday's decision, some firms are continuing to pause their decisions to invest or to hire people," he said.

"As I said before the referendum, this will have an impact on the economy and the public finances and there will need to be action to address that.

"But no-one should doubt our resolve to maintain the fiscal stability we have delivered for this country.

"To all companies large and small I would say this: the British economy is fundamentally strong, we are highly competitive and we are open for business."