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In a statement at Downing Street she said for EU leaders to reject her plan with no alternative at this "late stage of negotiations" was "not acceptable".
She said talks had reached an "impasse" and could only be unblocked with "serious engagement" from the EU side.
At an EU summit on Thursday, European Council President Donald Tusk said Mrs May's plan "will not work".
The pound's fall against the dollar and the euro deepened following Mrs May's statement.
The UK is due to leave the EU on 29 March 2019.
(source BBC NEWS)