* May to chair long cabinet meetings
* Brexit deadlock grips Britain
* Parliament fails to find a solution
* Ministers demand UK leave EU on April 12
By Guy Faulconbridge and William James
LONDON, April 2 (Reuters) - British Prime Minister Theresa May will chair a five-hour cabinet meeting on Tuesday in an attempt to plot a course out of the Brexit maelstrom as she comes under pressure to either leave the European Union without a deal or call an election.
Nearly three years since the United Kingdom voted to leave the EU in a shock 2016 referendum, British politics is in crisis and it is unclear how, when or if it will ever leave the club it first joined in 1973.
May’s deal has been defeated three times by the lower house of the British parliament which failed on Monday to find a majority of its own for any alternative to her deal. May is expected to try to put her deal to a fourth vote this week.
The deadlock has already delayed Brexit for two weeks beyond the planned exit date of March 29 and May is due to chair hours of cabinet meetings in Downing Street in a bid to find a way out of the maze.
“Over the last days a no-deal scenario has become more likely, but we can still hope to avoid it,” EU’s chief Brexit negotiator Michel Barnier said at an event in Brussels.
Education Secretary Damian Hinds said he hoped May’s withdrawal agreement would finally be approved this week by parliament, saying it remained the best outcome.
If May cannot get her deal ratified by parliament then she has a choice between leaving without a deal, calling an election or asking the EU for a long delay to negotiate a Brexit deal with a much closer relationship with the bloc.
“If we move quickly this week and we get this deal over the line it is still possible that we may be able to avoid having to have those European Parliament elections (in May),” Hinds said.
Asked whether there would be a much longer extension if May’s deal failed once again, he said: “That is absolutely a risk and a big looming risk at the moment.”
The Sun newspaper said Brexit-supporting ministers will demand May give a final ultimatum to fix the Irish backstop, the most controversial part of her deal, or see the United Kingdom leave without a deal at 2200 GMT on April 12.
The option which came closest to getting a majority in parliament on Monday was a proposal to keep Britain in a customs union with the EU, which was defeated by three votes.
A proposal to hold a confirmatory referendum on any deal got the most votes, but was defeated by 292-280.
The EU’s Brexit negotiator Michel Barnier said the only way to avoid a no-deal Brexit was if the British parliament found a majority for an option. He said the EU would accept a customs union and a Norway-style relationship.
Sterling fell almost 1 percent to $1.3036 on Monday.
The third defeat of May’s withdrawal agreement on Friday - the date Britain was originally scheduled to leave the EU - has left one of the weakest British leaders in a generation facing a spiralling crisis.
Her government and her Conservative Party, which has been trying to contain a schism over Europe for 30 years, are now riven between those who are demanding that May engineer a decisive break with the bloc and those demanding that she rule out such an outcome. (Writing by Guy Faulconbridge; editing by Michael Holden)