* May triggers formal Brexit divorce, says no turning back
* Two years of talks loom; exit planned in 2019
* United Kingdom's future unclear
* Brexit a major blow to European unity efforts
* May wants special ties, links trade and security (Adds Merkel quotes, European parliament)
By Guy Faulconbridge and Elizabeth Piper
LONDON, March 29 (Reuters) - Prime Minister Theresa May formally began Britain's divorce from the European Union on Wednesday, declaring there was no turning back and ushering in a tortuous exit process that will test the bloc's cohesion and pitch her country into the unknown.
In one of the most significant steps by a British leader since World War Two, May notified EU Council President Donald Tusk in a hand-delivered letter that Britain would quit the club it joined in 1973.
"The United Kingdom is leaving the European Union," May told parliament nine months after Britain shocked investors and world leaders by unexpectedly voting to quit the bloc. "This is an historic moment from which there can be no turning back."
The prime minister, an initial opponent of Brexit who won the top job in the political turmoil that followed the referendum vote, now has two years to negotiate the terms of the divorce before it comes into effect in late March 2019.
May, 60, has one of the toughest jobs of any recent British prime minister: holding Britain together in the face of renewed Scottish independence demands, while conducting arduous talks with 27 other EU states on finance, trade, security and other complex issues.
The outcome of the negotiations will shape the future of Britain's $2.6 trillion economy, the world's fifth biggest, and determine whether London can keep its place as one of the top two global financial centres.
For the EU, already reeling from successive crises over debt and refugees, the loss of Britain is the biggest blow yet to 60 years of efforts to forge European unity in the wake of two world wars.
Its leaders say they do not want to punish Britain. But with nationalist, anti-EU parties on the rise across Europe, they cannot afford to give London generous terms that might encourage other member states to break away.
May's notice of the UK's intention to leave the bloc under Article 50 of the EU's Lisbon Treaty was hand-delivered to Tusk in Brussels by Tim Barrow, Britain's permanent representative to the EU, on the top floor of the new Europa Building in Brussels.
That moment formally set the clock ticking on Britain's two-year exit process. Sterling, which has lost 25 cents against the dollar since the June 23 referendum, jumped to $1.25.
May signed the six-page Brexit letter on Tuesday night, pictured alone at the cabinet table beneath a clock, a British flag and an oil painting of Britain's first prime minister, Robert Walpole.
Her letter sought to set a positive tone for the talks though it admitted that the task of extracting the UK from the EU was momentous and that reaching comprehensive agreements within two years would be a challenge.
May wants to negotiate Britain's divorce and the future trading relationship with the EU within the two-year period, though EU officials say that will be hard.
"We believe it is necessary to agree the terms of our future partnership alongside those of our withdrawal from the EU," May told Tusk in her letter, adding that London wanted an ambitious free trade agreement with the EU.
"If, however, we leave the European Union without an agreement the default position is that we would have to trade on World Trade Organisation terms," she said.
May's most powerful European interlocutor, German Chancellor Angela Merkel, promised to take a "fair and constructive" approach to Brexit talks, but said Britain could negotiate its new relationship only after it untangles existing EU commitments.
"We must deal with many rights and obligations that have been linked to membership. Only then, later, can we talk about our future relationship."
May has promised to seek the greatest possible access to European markets but said Britain was not seeking membership of the "single market" of 500 million people as she understood there could be no "cherry picking" of a free trade area based on unfettered movement of goods, services, capital and people.
Britain will aim to establish its own free trade deals with countries beyond Europe, and impose limits on immigration from the continent, May has said.
In an attempt to start Brexit talks on a conciliatory note, May said she wanted a special partnership with the EU, though she laced that ambition with an a clear linkage of the economic and security relationship.
EU leaders will welcome assurances of a constructive approach, as well as an explicit recognition that Britain cannot retain the best bits of membership after leaving.
They may be less warm to an implication that Britain could live with a breakdown of talks on trade coupled with what might be seen as a threat to disrupt the security and counterterrorism cooperation for which Britain.
"We should work together to minimise disruption and give as much certainty as possible," May said. "Weakening our cooperation for the prosperity and protection of our citizens would be a costly mistake."
Tusk said the EU would seek to minimise the cost of Brexit to EU citizens and businesses and that Brussels wanted an orderly withdrawal for Britain.
"We already miss you," said Tusk who will send the 27 other states draft negotiating guidelines within 48 hours. "Thank you and goodbye."
In a draft resolution to be voted on next week, lawmakers in the European Parliament offered a faint glimmer of hope to the 48 percent of British voters who opposed Brexit, saying it was not too late for Britain to reverse the process.
U.S. President Donald Trump has been an enthusiastic proponent of Brexit, unlike his predecessor Barack Obama. White House spokesman Sean Spicer struck a neutral tone on Wednesday, saying Washington respected the will of British voters and backed a strong Britain and strong EU.
"Whatever future the UK-EU relationship looks like, we want the UK to remain a strong leader in Europe, for both the UK, the EU and Europe to remain strong leaders globally," Spicer said.
The course of the Brexit talks - and even their scope - are uncertain.
"The time frame is damn narrow," said Martin Schaefer, a spokesman for the German Foreign Ministry.
In recent months, German officials have made clear that they do not believe there is time to negotiate a bespoke transitional agreement for Britain that would come into force immediately after Brexit.
A huge number of questions remain, including whether exporters will keep tariff-free access to the single market and whether British-based banks will still be able to serve continental clients, not to mention immigration and the future rights of EU citizens in the UK and Britons living in Europe.
Adding more uncertainty, France and Germany both face elections this year.
"It’s bad news for everybody. It’s a wedge pushed into the European project," said French centrist presidential candidate Emmanuel Macron, who has made clear he would ensure Britain gains no undue advantages outside the Union.
At home, a divided Britain faces strains that could lead to its break-up. In the Brexit referendum, England and Wales voted to leave the EU but Scotland and Northern Ireland voted to stay.
Scottish nationalists have demanded an independence referendum that May has refused. In Northern Ireland, rival parties are embroiled in a major political crisis and Sinn Fein nationalists are demanding a vote on leaving the UK and uniting with the Republic of Ireland.
May said she knew that triggering Brexit would be a day of celebration for some and disappointment for others.
"Now that the decision to leave has been made and the process is under way, it is time to come together," she said.
Additional reporting by Alastair Macdonald, Jan Strupczewski and Yves Herman in Brussels, Michel Rose in Paris, Noah Barkin in Berlin and Kylie MacLellan, William James, Estelle Shirbon, Kate Holton, Paul Sandle and Anjuli Davies in London; Writing by Guy Faulconbridge; Editing by Mark Trevelyan, Peter Millership, Giles Elgood and Peter Graff