The United Kingdom's Labour party has agreed to support a further referendum on Brexit if it cannot first get changes to the Conservative government's deal or bring a general election.

Labour's stance comes as cross-party Brexit talks with the government enter a critical phase, with both sides insisting there is fresh impetus behind the attempt to find a consensus.

The latest cross-party talks are said to remain a long way off any breakthrough, but there has been a more "positive" tone and further meetings were held on Wednesday.

Downing Street is said to have set an informal deadline of the middle of next weekfor significant progress to be made.

Labour's divisions on Brexit were highlighted by disagreement over the party's European election manifesto, with leader Jeremy Corbyn keen to avoid the party being branded as pro-remain.

A statement released, after Labour's governing body met on Tuesday, said the party would "back the option" of a public vote, rather than keep it "on the table". But it rejected the idea of campaigning for a referendum under all circumstances – as supported by deputy leader Tom Watson and many ordinary members.

After cross-party Brexit discussions on Monday, Minister for the Cabinet Office David Lidington, said he was "encouraged", but that it would not be "sensible" to set a "hard and fast" deadline.

Labour's shadow environment secretary, Sue Hayman, said the two parties were "getting much more into the nuts and bolts of the detail", and that she believed the government was "open to moving forward in our direction".

Cross-party negotiations entered their fourth week after Prime Minister Theresa May's Brexit deal with the European Union was effectively rejected for a third time by members of Parliament.

Ministers insist their aim is to get MPs' approval for the terms of the UK's exit from the EU by May 22, so the country does not have to take part in elections to the European Parliament a day later.

Others involved in Monday's talks included, on the government side, Chancellor of the Exchequer Philip Hammond, Brexit Secretary Stephen Barclay, and Environment Secretary Michael Gove.

The Labour team included shadow Brexit secretary Keir Starmer, shadow chancellor John McDonnell and Hayman.

Labour had previously complained that the government appeared unwilling to move on a number of key areas, particularly on the possibility of a customs union with the EU after Brexit.

Areas of disagreement are also believed to include alignment of workers' rights and environmental protections.

Lidington said the prospect of a second referendum had been raised by Labour's contingent in the meeting.

"They know that this is not something that is government policy and that the last couple of times that it has come before the House of Commons it has been defeated," he said.

The EU has set a new deadline of Oct 31 for the UK's departure.