Brexit news: Theresa May formally resigns as Conservative leader, as Labour celebrates by-election win

Tory chairman Brandon Lewis said he was disappointed with the result, which saw his party drop to third place, but he pointed to a precedent of incumbent governments losing by-elections.

"Not winning any election is disappointing to me," he told Sky News.

"But the reality is, we're nine years into a Conservative Government, and I think you'll find no government in history has ever won a seat from the opposition nine years into government.

"That's the reality of it. It's always a tough backdrop to be fighting a by-election, particularly one where we're coming through that European election with the results we saw there."

Our overnight story says Theresa May will legally commit to ending Britain’s global warming contribution by 2050 – without caveats.

The result of the Peterborough by-election shows there is “no future” for  the Conservative Party until it delivers on Brexit, foreign secretary Jeremy Hunt has said.

He joined Tory leadership rivals including Boris Johnson, Matt Hancock and Dominic Raab in warning that failure to take the UK out of the European Union will hand power to Jeremy Corbyn.

Mr Corbyn visited the Cambridgeshire city to hail the victory of Labour’s Lisa Forbes as “a great win” which had “pushed the Tories to the margins” and shown widespread support for the party’s anti-austerity message.

My colleague Ashley Cowburn has been to the Downing Street lobby briefing, where the PM's spokesman was grilled about a story in the FT that the PM is locked in battle with Philip Hammond over a raft of spending announcements she had planned ahead of her departure.

A No10 spokesperson said: "In relation to some of the stories around today about this, I would just say the PM and chancellor obviously meet regularly to talk about spending and other issues, and you heard from the PM recently in setting out that for the remainder of her time in office she will we be focused on and delivering on the domestic agenda that she has put at the heart of her premiership since she became prime minister."

Asked if the chancellor raised objections, the spokesperson said: "They meet regularly to discuss spending priorities, I wouldn't get into the nature of discussions that they have."

Asked if it was legitimate for the PM to make spending commitments that a successor will have to find a way to fund, the spokesperson said: "I think we have said that for the remainder of her time in office she will be building on the domestic agenda that she has put at the heart oh her premiership ahead of any other not much further I could say on that - let's see what the next few weeks might bring."

Jeremy Corbyn is in Peterborough following his party's by-election victory.

He told Sky News: "We had a fantastic candidate, a fantastic campaign and the people of Peterborough rejected austerity and rejected the no-deal Brexit being offered by the Brexit Party.

"This win shows that Labour has the support across the piece, across the country and we are ready for a general election whenever it comes and we still stop the Tories taking this country into a no-deal Brexit with all the threats to jobs that holds."

Speaking to activists in the city, he praised Lisa Forbes, Labour's winning candidate, and said: "Write Labour off at your peril."

He fired off a message to "all the squabbling contenders" for the Tory leadership, shouting: "Bring it on. We are ready for a general election at any time and that general election will deliver a Labour government."

Three pro-EU Tories have come out in support of Sam Gyimah, who is an outsider in the leadership race.

Mr Gyimah, a former business minister, is the only candidate backing a Final Say referendum.

Nigel Farage has delivered a letter to No10 setting out his demands for Brexit - despite his party losing out to Labour the Peterborough by-election.

(Photo by Jeff J Mitchell/Getty Images)

Amidst the by-election fallout, Tory minister Jake Berry has been appointed as a junior minister at the Department for Business, Energy and Industrial Strategy.

He is also a junior minister at the Ministry of Housing, Communities and Local Government, where he looks after the Northern Powerhouse.

It appears he is replacing Richard Harrington at BEIS, who resigned in March in protest at the handling of Brexit.

BREAKING: Boris Johnson has won a High Court challenge against a court summons to face allegations of misconduct in a public office over claims made during the referendum campaign that the EU receives £350m a week from the UK.