The United Kingdom filed for divorce from the European Union on Wednesday, overturning four decades of integration with its neighbours, demolishing the notion that EU expansion is inevitable and shaking the foundations of a bloc that is facing challenges to its identity and its place in the world.

In Brussels, Britain's top envoy to the EU, Tim Barrow, hand-delivered a letter to European Council President Donald Tusk formally triggering a two-year countdown to the final split.

There is "no reason to pretend this is a happy day," Tusk told reporters later, emphasizing that the priority now is to minimize costs for EU citizens and member states.

To Britain, he said: "We already miss you."

U.K. Prime Minister Theresa May insisted that Britain is not turning its back on Europe. She said the U.K. wants "a new and equal partnership" with "our friends and allies in the EU." She wants the U.K.'s exit to be "smooth and orderly."

"This is an historic moment from which there can be no turning back," May told legislators in the House of Commons. "Today the government acts on the democratic will of the British people."

The reality of Brexit6:12

For Britons who voted to leave the bloc in a referendum nine months ago, it was a time for celebration.

"In my opinion, this is the greatest moment in modern British history," said Brendan Chilton, general secretary of the pro-Brexit group Labour Leave. "We are finally beginning the process by which we leave the European Union, restore our Parliament and once again become a sovereign nation."

For "remain" campaigners, it was time to fight for a divorce settlement that preserves what they see as key benefits of EU membership, including free trade in goods and services and the right to live and work anywhere in the bloc.

"The phoney war is over," said Joe Carberry, co-director of the pro-EU pressure group Open Britain. He said Britain had decided that it would leave the bloc — but "the issue of how we will leave, and the democratic checks and balances along the process of the negotiations, remains unresolved."

For Jean-Claude Juncker, president of the European Commission, Britain's departure is "a failure and a tragedy."

EU will 'act as one'

European Union leaders say they will remain united and strive to protect the bloc's interest following Britain's decision.

"The Union will act as one and preserve its interests," the leaders said in a statement Wednesday. "Our first priority will be to minimize the uncertainty caused by the decision of the United Kingdom for our citizens, businesses and member states."

They said they would "start by focusing on all key arrangements for an orderly withdrawal."

The leaders will meet in Brussels on April 29.

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Britain's Prime Minister Theresa May announced to Parliament that Britain formally filed for divorce from the European Union Wednesday. (Parliamentary Recording Unit/Associated Press)

Tumultuous time ahead

The loss of a major member is destabilizing for the EU, which is battling to contain a tide of nationalist and populist sentiment and faces unprecedented antipathy from the new resident of the White House.

It is even more tumultuous for Britain. For all the U.K. government's confident talk of forging a close and friendly new relationship with its neighbours, it cannot be sure what its future relationship with the bloc will look like — whether businesses will freely be able to trade, students to study abroad or pensioners to retire with ease in other EU states. Those things have become part of life since the U.K. joined what was then called the European Economic Community in 1973.

It's not even certain that the United Kingdom will survive the exit intact.

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A cake presented by Britain's UK Independence Party (UKIP) celebrates the official triggering of Article 50 of the Lisbon Treaty in Brussels on Wednesday. (Thierry Monasse/Associated Press)

Scotland's parliament voted Tuesday to back First Minister Nicola Sturgeon's call for a referendum on independence within two years. Scottish voters backed remaining in the EU in last year's vote, and Sturgeon insists Scotland must not be "taken down a path that we do not want to go down without a choice."

May insists "now is not the time" for a referendum, setting her on course for a showdown with the Edinburgh administration just when the U.K. government wants to devote all its energies to the EU talks.

The two sides now have until March 2019 to agree on a divorce settlement and — if possible — establish a new relationship between Britain, the world's fifth-largest economy, and the EU, a vast single market stretching over 27 countries and half a billion people.

Brexit Secretary David Davis — the man charged with leading Britain's side in the talks — has called it "the most complicated negotiation in modern times, maybe the most complicated negotiation of all time."

'How do we do this?'

Tusk has said that within 48 hours he will respond with a draft negotiating guidelines for the remaining 27 member states to consider. Then, leaders of those nations meet next month to finalize their negotiating platform before instructing the EU's chief negotiator, French diplomat Michel Barnier.

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Tim Barrow, the U.K.'s permanent representative to the EU, arrives at the Europa building in Brussels earlier on Wednesday. Barrow hand-delivered a letter giving formal notice of the U.K.'s Brexit plans to the EU Council president Donald Tusk. (Virginia Mayo/Associated Press)

Then Barnier will sit down with his British counterpart, Davis, who has said the first item on the agenda will probably be: "How do we do this?"

As in many divorces, the first area of conflict is likely to be money. The EU wants Britain to pay a hefty bill — Juncker put it at around 50 billion euros ($63 billion US) — to cover pension liabilities for EU staff and other commitments the U.K. has agreed to.

British negotiators are sure to quibble over the size of the tab.

Davis said Monday that Britain will "meet our international obligations," but added: "I don't think we are going to be seeing that sort of money change hands."

Juncker has said the EU will not try to punish Britain for leaving.

"I do not think we will get anywhere by clobbering the British, insulting them and driving too hard a bargain," he said in a speech this month. But, he added, "There can be no cherry picking either ... You are either in or out."

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Anti-Brexit protesters, one wearing a giant Theresa May head, hold placards outside the U.K. Parliament where the start of the Brexit process was triggered today. (Stefan Wermuth/Reuters)

Free movement to be major sticking point

Negotiations will soon hit a major contraction: Britain wants "frictionless" free trade, but says it will restore control of immigration, ending the right of EU citizens to live and work in Britain. The EU says Britain can't have full access to the single market if it doesn't accept free movement, one of the bloc's key principles.

Both Britain and the EU say a top priority will be guaranteeing the rights of 3 million EU citizens living in Britain, and 1 million Britons living elsewhere in the bloc.

European Union president swallows bitter Brexit pill1:02

The two sides also appear to disagree on how the talks will unfold. EU officials say the divorce terms must be settled before negotiators can turn to the U.K.'s future relationship with the bloc. British officials want the two things discussed simultaneously.

May has suggested that if talks stall she could walk away, saying that "no deal for Britain is better than a bad deal for Britain."

That prospect alarms many British businesses. If Britain crashed out of the EU without a trade deal it would fall back onto World Trade Organization rules, meaning tariffs and other barriers to trade.

Even if talks go well, EU leaders say there is little chance a final agreement on relations between the two parties will be reached by 2019. Some say it could take a decade.