The latest talks between ministers and Labour to try to end the Brexit impasse were “positive” and “productive”, the PM’s de facto deputy has said.

Speaking afterwards, David Lidington said he was “encouraged” by a sense from both sides about the “need to inject greater urgency” into the talks.

He said there would be further meetings between the parties this week.

Labour’s shadow environment secretary Sue Hayman said there had been “really constructive discussion” on Monday.

She 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 have been taking place for a number of weeks after Theresa May’s Brexit deal with the EU was effectively rejected for a third time by MPs.

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

To that end, No 10 says it wants to introduce the Withdrawal Bill – legislation required to implement the withdrawal deal – to Parliament as soon as possible, but Downing Street said that process would not begin until it had a “realistic prospect of securing passage”.

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Monday’s talks were led on the government side by Chancellor Philip Hammond, Brexit Secretary Stephen Barclay and Environment Secretary Michael Gove.

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

Cabinet Office Minister Mr Lidington has said it would not be “sensible” to set a “hard and fast” deadline for the talks, warning that it would become a “cliff edge in itself that ramps up expectations”.

But BBC political editor Laura Kuenssberg said discussions appeared to have gone better than on previous days.

The sides are a long way off any breakthrough – and it is fair to say expectations are low that there will actually be a deal in the end – but the mood at least seems better, she added.

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Ms Hayman confirmed that a “public vote” on Brexit had been on the agenda for all of their meetings and Labour was “exploring ways in which we can work with the government on this”.

Bur Mr Lidington said it was not government policy and that the proposal had been voted down in the House of Commons.

Earlier Shadow Attorney General Shami Chakrabarti said Labour front benchers involved in the talks must tell the party’s ruling national executive committee on Tuesday “whether there is any hope for sensible Brexit”, or whether the only means of breaking the deadlock looks to be a second referendum or a general election.

The EU has set a new deadline of 31 October for the UK’s departure.

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