The EU's three most populous continental nations signalled that the UK must first take the plunge of invoking Article 50 to exit before it can negotiate its future trade and other ties with the bloc.
Chancellor Angela Merkel - hosting French President Francois Hollande and Italian Prime Minister Matteo Renzi in Berlin - said that "we agreed on this, that there will be no informal or formal talks on the exit of Britain until an application has been filed to leave the European Union".
British finance minister George Osborne had said earlier that his country should only activate Article 50 when it has a "clear view" of its future relations with the bloc.
Merkel also stressed that "there must be no period of uncertainty" that is prolonged, and that the EU must counter "centrifugal forces" in other EU countries pushing to leave the union.
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"Uncertainty generates often irrational behaviour. Uncertainty also leads financial markets to act irrationally"
Hollande, somewhat more bluntly, urged Britain to "not waste time" in triggering the process to leave, arguing that it was to all parties' benefit to move forward quickly.
"Being responsible means not wasting time -- not wasting time in dealing with the question of Britain's departure, not wasting time too in putting in place the new stimulus that we need to give to the European Union, that is to say, the 27 members."
"Because nothing is worse than uncertainty," he added. "Uncertainty generates often irrational behaviour. Uncertainty also leads financial markets to act irrationally."
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'Delivering prosperity'
In a joint statement the leaders said they "regret that the United Kingdom will no longer be our partner within the European Union" but said confidently that the EU "is strong enough to find the right answers".
On the eve of a Brussels summit, they urged steps among the remaining 27 members to jointly boost cooperation on internal and external security as well as the economy and programmes to help youths.
Merkel vowed that the remaining members would push on with the European project, saying that "we will suggest to our (EU) colleagues that we should put in place a new impulse ... in the coming months".
She called for unity and urged a new collective push for cooperation in areas that included "defence, growth or jobs and competitiveness".
The focus should be on internal and external security, counter-terrorism and protecting the EU's external borders, she said, adding that "a second focus is on the economy, growth and competitiveness".
Renzi said that "it is clear that we have to respect the sovereign decision of the British people but at the same time, there has to be a strategy for the months to come".
German Chancellor Angela Merkel Source: AAP
"We are a big family and we need to reassure the members of the family. But there is also a great need to remodel the European project in the coming years... Things need to move forward."
In their joint statement the three leaders said they would push for greater cooperation on security issues, including "developing our European defence and taking necessary engagements on joint operations".
They also said Europe must "keep its promise on delivering prosperity to its citizens".
To do so, eurozone nations should "take new steps if necessary to reinforce growth, competitiveness, employment, and convergence including in the social and fiscal areas".
A key target group would be to reduce massive youth unemployment in several EU nations, they said, stressing that "Europe would not succeed unless it gives hope to its youth".
The proposed reforms would be the subject of a September summit, with a view to the implementing them within six months.
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Cameron seeks to calm Britain
In his first appearance before a sombre House of Commons since the referendum, Cameron told lawmakers he wanted to retain the "strongest possible economic links with our European leaders".
"Britain is leaving the European Union, but we must not turn our back on Europe -- or on the rest of the world," he added.
He also announced the creation of a new government unit that will plan Britain's withdrawal from the EU -- a first for a European Union member state.
In one of the first big signs of the damage caused by the Brexit vote, Standard and Poor's downgraded Britain's cherished AAA credit rating -- the highest possible -- to AA due to "continued uncertainty" following the decision.
The pound fell to its lowest level for three decades against the dollar while stock markets in the US and European continued to fall.
Another source of uncertainty is who will replace Cameron as prime minister and leader of the Conservative party.
The leaders of the Conservative committee which runs the process recommended Monday that his replacement be installed by September 2 at the latest. Nominations for the post formally close on Thursday.
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Leading Brexit campaigner and ex-mayor of London Boris Johnson and Home Secretary Theresa May, who wanted Britain to stay in the EU but is seen as a unifying candidate, are the current favourites.
Like Cameron, Johnson sought to emphasise continuity in a column for the Daily Telegraph newspaper.
"I cannot stress too much that Britain is part of Europe, and always will be," he said.
He also attempted to reach out to the 48 per cent of Britons who voted to stay in the EU, urging Brexit supporters to "build bridges" with pro-EU "neighbours, brothers and sisters".
The main opposition Labour party could also be getting a new leader after a revolt against veteran socialist Jeremy Corbyn, who has been criticised for his lacklustre role in the campaign to keep Britain in Europe.
Two-thirds of his shadow cabinet team have quit and he faces a vote of no confidence.
However, around 2,000 of the young grassroots activists who voted Corbyn in last year gathered outside parliament to show their continued support for him, brandishing placards with slogans such as "Corbyn In, Tories Out".
There will be a secret ballot of Labour MPs on a no-confidence motion on Corbyn, the result of which will be announced on Tuesday, but it would still be up to the broader ranks of party members whether he goes or not.
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Stand up against hate crimes
Britain's historic decision to leave the 28-nation bloc has also fuelled fears of a break-up of the United Kingdom, with Scotland eyeing a new independence poll.
Cameron's spokeswoman played down the announcement by Scottish First Minister Nicola Sturgeon that a second independence referendum was now "on the table" despite a vote against secession in 2014.
"The reasons for Scotland to be in the UK are as strong now as they were 18 months ago," the spokeswoman said, adding: "The last thing Scotland needs now is another divisive referendum".
Cameron also condemned a wave of xenophobic attacks which took place in Britain over the weekend, including on a Polish community centre in London following the vote, calling on the country to unite.
"We will not stand for hate crime or these kinds of attacks. They must be stamped out," he said.
