After failing three times to get parliament's approval for her Brexit deal, the government will now put the bill, legislation which will enact that deal, before parliament for a vote in early June.

"Whatever the outcome of any (indicative) votes, I will not be simply asking MPs to think again," May wrote in the Sunday Times newspaper.

"Instead I will ask them to look at a new and improved deal with a fresh pair of eyes - and to give it their support."

The newspaper said May would consult cabinet colleagues on proposed changes to the withdrawal agreement aimed at securing cross-party support.

It said the cabinet would also consider plans for a series of indicative votes to establish which proposals can command a majority in parliament.

Nearly three years after the United Kingdom voted 52 per cent to 48 per cent in a referendum to leave the EU, it remains unclear how, when or even if the country will leave the European club it joined in 1973.

The current deadline to leave is October 31.

Brexit talks between May's Conservatives and the opposition Labour Party collapsed on Friday hours after May agreed to set out in early June a timetable for her departure.

On Saturday Labour's Brexit spokesman Keir Starmer said the government should put a promise to hold a further public vote on the face of the Withdrawal Agreement Bill to break the Brexit impasse.

Australian Associated Press