LONDON (AP) — Britain filed for divorce from the European Union on Wednesday, with fond words and promises of friendship that could not disguise the historic nature of the schism — or the years of argument and hard-nosed bargaining ahead as the U.K. leaves the embrace of the bloc for an uncertain future as "global Britain."

Prime Minister Theresa May triggered the two-year divorce process in a six-page letter to EU Council President Donald Tusk, vowing that Britain will maintain a "deep and special partnership" with its neighbors in the bloc. In response, Tusk told Britain: "We already miss you."

May's invocation of Article 50 of the EU's key treaty sets the clock ticking on two years of negotiations until Britain becomes the first major nation to leave the union — as Big Ben bongs midnight on March 29, 2019.

The U.K.'s departure could not come at a worse time for the EU, which has grown from six founding members six decades ago to a vast, largely borderless span of 28 nations and half a billion people. Nationalist and populist parties are on the march across the continent in revolt against the bloc's mission of "ever-closer union." And in Washington, President Donald Trump has derided the EU, NATO and other pillars of Western order built up since World War II.

"This is an historic moment from which there can be no turning back," May told lawmakers in the House of Commons, moments after her letter was hand-delivered to Tusk in Brussels by Britain's ambassador to the EU, Tim Barrow.

In the letter, May said the two sides should "engage with one another constructively and respectfully, in a spirit of sincere cooperation."

But for all the warmth, the next two years will be a tough test of the notion that divorcees can remain good friends.

May is under pressure from her Conservative Party and Britain's largely Euroskeptic press not to concede too much in exchange for a good trade deal with the EU. For their part, the other 27 members of the bloc will need to stick together and stand firm as they ride out the biggest threat in the union's history.

Brexit has been hailed by populists across Europe — including French far-right leader Marine Le Pen — who hope the U.K. is only the first in a series of departures. EU leaders are determined to stop that happening.

"The European Union is a historically unique success story," German Chancellor Angela Merkel said in Berlin. "It remains one even after Britain's withdrawal. We will take care of that."

Britons voted 52 percent to 48 percent in favor of leaving the bloc in a referendum nine months ago, and they remain deeply divided over Brexit.

In the pro-Brexit heartland of Dover on England's south coast — whose white cliffs face toward France — some were jubilant as May pulled the trigger.

"I'm a local church minister, and I said to my wife, 'All I want to do before I die is see my country free from the shackles of Europe,'" said 70-year-old Mike Piper, buying a copy of the Sun tabloid with the front-page headline "Dover and Out."

Former UKIP leader Nigel Farage, who campaigned for years to take Brexit from a fringe cause to a reality, said Britain had passed "the point of no return."

"I can still, to be honest with you, scarcely believe today has come," he said.

But many young Britons — who have grown up in the EU and voted overwhelmingly for Britain to remain a member — worried about how much they would lose.

"I'm really anxious about it. It was a bad idea," said Elaine Morrison, an 18-year-old who was traveling to Barcelona with friends. "I like traveling to other countries And it will be a trouble now. The pound is weaker so it will cost more to buy the euros, and the costs of travel will be more expensive. And there will be red tape."

People in London's financial district, the City, were anxious about the uncertainty.

"No one knows how this is going to go," said City worker Nicola Gibson. "It's a gamble, it's a risk."

May's six-page letter to Tusk was conciliatory, stressing that Britons want to remain "committed partners and allies to our friends across the continent."

But there was a hint of steel in May's assertion that without a good deal, "our cooperation in the fight against crime and terrorism would be weakened."

That could be seen by some in Europe as a threat to withdraw British security cooperation if the U.K. does not get its way.

European Parliament Brexit coordinator Guy Verhofstadt responded diplomatically: "I cannot, as a gentleman, even imagine that a lady as Mrs. May is using blackmail, is thinking of blackmail."

Tusk said he will respond by Friday with draft negotiating guidelines for the remaining 27 member states to consider. They'll meet April 29 to finalize their platform. Talks between the EU's chief negotiator, French diplomat Michel Barnier, and his British counterpart, Brexit Secretary David Davis, are likely to start in the second half of May.

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

Britain acknowledges it will have to pay something, but is sure to quibble over the size of the tab. May did not indicate Wednesday how much Britain would be willing to pay, saying only that it will no longer pay "significant sums of money on an annual basis" to the EU.

But, May added: "We're a law-abiding nation. We will meet obligations that we have."

Negotiations will also soon hit a major contraction: Britain wants to strike "a bold and ambitious free trade agreement" with the bloc of some 500 million people, 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. In her letter, May said "we should aim to strike an early agreement about their rights" — but for now they remain in limbo.

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, while Britain wants the two things discussed simultaneously.

Britain wants to seal a new trade deal within two years, but Verhofstadt told The Associated Press there would have to be a further transition period of "no more than three years to discuss, to detail the content of this future."

A final deal must be approved by both the British and European parliaments — and Verhofstadt said EU lawmakers "will use our veto power" if they do not like the outcome.

Brexit has profound implications for Britain's economy, society and even unity. The divisive decision has given new impetus to the drive for Scottish independence and shaken the foundations of Northern Ireland's peace settlement. Scottish First Minister Nicola Sturgeon, who says the Brexit vote means Scotland should get a referendum on independence, accused May of making "a reckless gamble."

But anti-EU politicians saluted Wednesday as the day Britain regained its sovereignty from Brussels bureaucrats.

"If you've been locked inside a dark and cramped dungeon and you step out into sunlight, it's going to be a bit intimidating," pro-Brexit lawmaker Douglas Carswell said. "We as a country have got to rediscover the art of self-governance."

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Follow Jill Lawless on Twitter at http://Twitter.com/JillLawless

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Casert reported from Brussels. Associated Press writers Danica Kirka, Siobhan Starrs and Jonathan Shenfield in London, Lorne Cook in Brussels, Geir Moulson in Berlin, Jan M. Olsen in Copenhagen and Monika Scislowska in Warsaw contributed to this report.