Boris Johnson, the leading "Leave" campaigner, former London mayor and favourite to become the next Conservative prime minister, sought to calm fears about Britain's economic future, saying it would continue to have access to the EU single market.
But Johnson did not explain how he planned to secure free trade with Europe without sacrificing some of the main promises that "Leave" campaigners made to voters, notably that Britain would be able to cut immigration and free itself from regulations set in Brussels.
As Europe Correspondent Brett Mason reports, British politicians are in damage control tonight as they try to limit the chaos caused by the vote to leave the European Union.
The Chancellor offered his reassurances in an early morning address before the markets opened, and the Prime Minister is holding a cabinet meeting - before parliament reconvenes.
Britain's Prime Minister David Cameron is expected to stay on in a caretaker role until the UK Conservative Party elects a new leader in about three months, after he resigned on Friday.
But he has refused to invoke Article 50 of the EU's Lisbon Treaty, which allows for two years of exit negotiations, leaving little clarity about how or when Britain will begin negotiations with the EU on a new relationship.
In the referendum, voters ignored Cameron's appeals to stay in the EU by 52 per cent to 48 per cent, delivering the biggest blow since World War Two to the European project of forging greater unity.
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Cameron is expected to meet the other 27 EU leaders at a summit in Brussels on Tuesday.
British Finance Minister George Osborne, who had warned during the campaign that a "Brexit" would cause financial market volatility, scheduled a statement for 7am (local time) on Monday to provide reassurance about "financial and economic stability".
Cameron's Conservatives have been at war with each other for years over whether to quit the EU. But the vote to leave a bloc that Britain joined 43 years ago also pushed the UK Labour party into chaos over the weekend.
Senior Labour Party parliamentarians withdrew backing for their leader after traditional supporters rejected the party's pro-EU stand in droves.
Scotland's leader promised she would do whatever it takes to keep her strongly pro-EU country in the bloc, including potentially vetoing legislation on a British exit.
French President Francois Hollande declared there was no going back on "Brexit", saying: "What was once unthinkable has become irreversible".
Hollande said France and Germany must use their strong friendship to seize the initiative, warning that "separated, we run the risk of divisions, dissension and quarrels".
He and Chancellor Angela Merkel discussed the issue by phone and an aide said they were in "full agreement on how to handle the situation".
The EU is preparing to move its European Banking Authority from London following Britain's vote to leave the Union, EU officials said on Sunday, setting up a race led by Paris and Frankfurt to host the regulator.
The United States, which had made clear it wanted Britain to stay in the EU, also showed signs of unease. US Secretary of State John Kerry will visit Brussels and London on Monday.
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Osborne said it was "inevitable" the economy would have to adjust following the Brexit vote but he would do "everything I can" to make it work.
He warned it "would not be plain sailing" but the UK was "equipped for whatever happens".
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In a message to nervous firms and investors, Osborne stressed the UK economy was "fundamentally strong" and "open for business".
Osborne said he would address his future role in the Conservative Party "in the coming days".
The pound fell in Asian markets on Monday amid fears of the consequences of the vote to leave the EU. Political turmoil has roiled the UK, as leaders grappled with the question of how precisely Britain would separate from the other 27 nations in the EU.
Germany, Britain and France will be meeting later on Monday to discuss the decision.
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An emergency budget to deal with the fallout from the EU vote looks unlikely to take place until later in the year, as the chancellor said it was better to delay action to shore up the public finances until a new prime minister is in place.
Following talks over the weekend with Bank of England Governor Mark Carney and fellow finance ministers and international economic organisations, Osborne said that "further well-thought through contingency plans" were ready to be deployed if needed in response to further volatility.
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Osborne - who has kept a low public profile since the Brexit vote - said it was "inevitable" that the UK economy would face an "adjustment" in the wake of the Brexit vote, though he steered clear of repeating explicit warnings of recession made during the referendum campaign.
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He said 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 David Cameron as prime minister.
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"The British people have given us their instructions," Osborne said. "There is much to do to make it work ... my colleagues and I are determined to do the best for Britain."
