European Union chief Brexit negotiator Michel Barnier speaks during a debate on Brexit at the European Parliament in Strasbourg, eastern France. Picture: Jean-Francois Badias/AP

Strasbourg, France - The risk of Britain leaving the European Union without an exit deal has never appeared higher, EU Brexit negotiator Michel Barnier said the morning after the British parliament emphatically rejected a divorce deal with Brussels.

"We are just 10 weeks away from the end of March, that is, the moment chosen by the British government to become a third country," Barnier told EU lawmakers in the French city of Strasbourg.

"Today, with 10 weeks to go, the risk of a no-deal has never seemed so high," he added.

"It is now for the British government to clarify how the United Kingdom wants to proceed to organize the orderly withdrawal that it requested," Barnier added.

Late Tuesday, lawmakers delivered the worst defeat for a British government in decades by voting by 432 to 202 against the withdrawal deal Prime Minister Theresa May struck with Brussels.

Britain is due to leave the EU on March 29. Without a deal, EU rules would cease to apply in Britain overnight.