Talks between Labour and the government aimed at breaking the Brexit impasse have ended without an agreement.

Jeremy Corbyn blamed what he called the government’s “increasing weakness and instability”, saying the discussions had “gone as far as they can”.

No 10 said progress had been made in some areas, but the talks, which began six weeks ago, had been “challenging”.

The PM has promised to set a timetable for leaving Downing Street following a Brexit vote next month.

Theresa May will try once again to win the support of MPs in the week beginning 3 June, when the Commons votes for the first time on the EU Withdrawal Agreement Bill – the legislation needed to implement her deal with the EU.

Brexit had been due to take place on 29 March – but after MPs voted down the deal Mrs May had negotiated with the bloc three times, the EU gave the UK an extension until 31 October.

This prompted negotiations between the Tories and Labour to see if the parties could come to a Brexit agreement, despite differences over issues including membership of a customs union and a further referendum.

In a letter to the prime minister, Labour leader Mr Corbyn said the move towards choosing her replacement meant “the position of the government has become ever more unstable”.

He later told reporters that his party had negotiated “in good faith and very seriously, and put forward a lot of very detailed arguments”, which he thought was “the responsible thing to do”.

But, he added: “The issue [is] that the government has not fundamentally shifted its view and the divisions in the Conservative Party mean the government is negotiating with no authority and no ability that I can see to actually deliver anything.”

The Labour leader also said “very little” discussion had taken place between the parties about putting a range of options to MPs to break the Brexit deadlock.

The prime minister’s official spokesman said: “We have made real progress on some issues such as workers’ rights and environmental protections, but it is clear that we are not going to be able to reach a complete agreement.

“In particular, there have been very challenging discussions in respect of the different positions of the two sides on customs and the holding of a second referendum.”

The spokesman added that Mrs May “continued to believe it is the duty of elected politicians to deliver on the result of the referendum”.