Prime Minister Theresa May yesterday warned MPs against supporting a second Brexit referendum, as calls mount for a public vote to break the political impasse over the deal she struck with the EU.

"Let us not break faith with the British people by trying to stage another referendum," she told parliament.

"Another vote... would do irreparable damage to the integrity of our politics," she said, adding that a second vote "would likely leave us no further forward".

Former foreign secretary Boris Johnson, a leading Brexit campaigner, also said that anyone considering a second referendum was "out of their minds".

"A second referendum would provoke instant, deep and ineradicable feelings of betrayal," he wrote yesterday in his weekly column in the Daily Telegraph.

Britain voted to leave the European Union in a shock referendum in 2016 and is set to leave on March 29 next year, although May is struggling to persuade parliament to accept a divorce agreement she struck last month.

EU leaders have ruled out any renegotiation of the deal agreed after tortuous negotiations with London.

May last week survived a confidence vote initiated by members of her own Conservative Party because of her Brexit strategy but she is badly weakened after a third of her parliamentary party voted to be rid of her.

In the face of calls for a second referendum to resolve the impasse, she has argued that this would betray the 2016 result and undermine public confidence in politics.