* EU leaders conclude May has little chance of success
* April 12, or May 22, loom as next Brexit deadlines
* UK parliament divided on how, when or whether to leave (Updates on leaders' talks)
BRUSSELS, March 21 (Reuters) - British Prime Minister Theresa May failed to reassure European Union leaders on Thursday that she can secure a deal at home next week on an orderly Brexit, diplomats said, prompting frantic talks on how to ease Britain out without a deal.
As seven hours of talks on Brexit ended, European Council President Donald Tusk tweeted that the other 27 leaders had agreed unanimously on their response to Britain's requests.
With just a week left until Britain is due to quit the bloc, leaders scrapped planned talks on Chinese trade and plunged into six hours of talks through the evening on setting new deadlines that would avoid Britain crashing out of the block next Friday -- but also avoid prolonging uncertainty.
One option could see Britain lurch out in just three weeks, on April 12, unless it overcomes deep divisions to request a long extension that will involve taking part in EU elections on May 23. Another, if May succeeds in winning backing for a deal, would see it enter a post-EU transition on May 22.
Grilled for over an hour by the other 27 leaders at a Brussels summit, May insisted she could win parliamentary backing next week for the deal that would ease Britain out on terms she agreed with the EU last year. But far from reassuring them, many concluded that she herself had little faith in overturning two previous heavy defeats by lawmakers in London.
"It did not go well," said one EU official familiar with the talks. "They basically realized that she doesn't really believe it herself. They don't want to be seen to be forcing the Brits out now. But they are looking for ways to end the agony."
Following six hours of talks after May left the room, diplomats said leaders were still wrangling over possibilities.
A draft statement seen by Reuters, still not final, said that if May succeeds against the odds in parliament, Britain would leave not on March 29 but by May 22, a day before the EU starts elections for a new European Parliament. Those two months would give Britain time to pass necessary legislation.
If May fails, Britain could ask for a long delay -- possibly, though not explicit, until at least the end of the year or much longer. But it could only get that if it holds its own EU election. Under UK law, that election must be announced six weeks beforehand, on April 12. If by then, it had failed to call an election, it would be ejected from the Union forthwith.
"That way Merkel and the rest of the EU can avoid blame for forcing the British out," one EU official said. "It will be up to the British themselves to say they are leaving with no deal."
Such an outcome is likely to inflict substantial economic damage not just on Britain, but also on Europe as a whole, notably neighbors Ireland, the Low Countries and France. EU leaders facing elections and a rise of populist nationalists at the elections are keen to pin any blame for that on the British.
Leaders arrived in Brussels expecting to put off major decisions, assuring May of the "technical" extension if she won next week's vote but leaving hard decisions about what to do if she fails until a possible emergency summit before next Friday.
However, after her unconvincing presentation at the start of the meeting, they decided they needed to move faster on "Plan B" -- though a British source described the atmosphere as fair.
MACRON TALKS TOUGH
French President Emmanuel Macron took a hard line, reflecting fears that Britain, long a drag on Paris's goals of deeper European integration, would hang around inside the bloc for months or years. That, some say, could distract it from other issues and foster rising anti-EU nationalism.
Voicing more clearly the fears of business that a no-deal Brexit would hurt economies across the continent, German Chancellor Angela Merkel was arguing for caution.
Macron told reporters before the meeting: "In the event of another 'no' vote in Britain, we will be heading towards a 'no- deal'. Everyone knows it."
Merkel vowed to "work to the last minute" to avoid a disorderly withdrawal.
The 27 have shown remarkable unity on Brexit since Britons voted three years ago to leave. But the strain of deciding how to manage a "cliff edge" exit for the British economy brought the top leaders into animated discussion for the first time.
Diplomats said some of the harder brinkmanship from the continent should be seen partly as intended to pressure British members of parliament to back May's deal or face chaos. "But there is a real risk of an accidental hard Brexit," one warned.
May has said delaying Brexit beyond June would be a failure to deliver on the Brexit referendum of three years ago. So any choice to go for a longer delay might be accompanied by her stepping down and paving the way for a major political shake-up in London.
An address to the nation in which she blamed parliament for a failure to secure Brexit appeared to irritate the very lawmakers she needs to win over next week.
May said she was still working on support for her deal, which envisages negotiating a bespoke close relationship with the EU that keeps Britain outside its customs union or single market.
"I am still working on ensuring that parliament can agree a deal so that we can leave in an orderly way," she told reporters.
"A short extension would give parliament the time to make a final choice that delivers on the result of the referendum."
But positions have hardened after a chaotic week when the parliament's speaker questioned whether she could even bring her deal to a third vote. (Reporting by Robin Emmott, Gabriela Baczynska, Elizabeth Piper, Richard Lough, Anthony Deutsch, Philip Blenkinsop, Giulia Paravicini, William James, Thomas Escritt, Jan Strupczewski and Alastair Macdonald in Brussels and Guy Faulconbridge and Kylie MacLellan in London Writing by Alastair Macdonald, Jan Strupczewski and Elizabeth Piper; Editing by Kevin Liffey and Alastair Macdonald)