Brexit talks between Prime Minister Theresa May's Conservatives and the opposition Labour Party are about to close without an agreement, the BBC said on Friday.

May and Labour leader Jeremy Corbyn will now move to a second phase, aimed at agreeing on a process for parliamentary votes designed to find a consensus, the BBC said.

May announced on April 2 that she would open talks with Labour but the two parties have failed to agree on major issues such as Labour's demand for a post-Brexit customs union.

May agreed on Thursday to set out a timetable for her departure in early June after the latest attempt to get her thrice defeated Brexit deal approved by parliament.

Nearly three years since the United Kingdom voted to leave the European Union in a shock referendum result, it is still unclear how, when or if it will ever indeed quit the European club it first joined in 1973.

Brexit referendum more likely if talks collapse

Another referendum on European Union membership is more likely if talks between Prime Minister Theresa May's government and the opposition Labour Party collapse, an influential Labour lawmaker said on Friday.

"If the talks are not going anywhere, from my point of view that leads to only one conclusion," Hilary Benn, the chairman of parliament's Brexit committee, told BBC radio.

"There are only two ways out of the Brexit crisis that we've got: either parliament agrees a deal or we go back to the British people and ask them to make the choice.

"And I think this brings the prospect of a confirmatory referendum closer although there's not yet a majority for that in parliament," he said.