THERESA May faced calls to quit from senior Tories after their party suffered a humiliating net loss of more than 1,300 seats in England’s local council elections; the Conservatives’ worst defeat since 1995.

But there was also anger within Labour ranks at Jeremy Corbyn’s leadership after the party also suffered the effects of a Brexit backlash from voters, losing almost 80 seats.

The chief beneficiary of the shift of support was the pro-Remain Liberal Democrats, who picked up a net gain of more than 670 seats. Greens also fared well, winning almost 200 council seats, as did Independents.

The results have piled pressure on the Tory and Labour leaderships to seal a compromise deal on Brexit when both parties resume talks on Tuesday. Hundreds of voters spoiled their ballot papers in protest at the continuing deadlock.

The mood at Westminster in recent days has been increasingly optimistic as politicians from both sides have talked up the prospect of an historic agreement that would mean Britain leaving the EU within weeks.

Following the council results, Mr Corbyn acknowledged the public had sent a “very clear” message that they wanted MPs to “get a deal done” on Brexit.

Ahead of the poll, his party had boasted how the results would show Labour was poised to take power; John McDonnell, the Shadow Chancellor, even predicted his party might pick up as many as 400 seats.

But as most of the results were in, a sombre-looking Labour leader said they meant there was a “huge impetus on every MP and they’ve all got that message, whether they themselves are Leave or Remain…that an arrangement has to be made, a deal has to be done, Parliament has to resolve this issue. That is very, very clear”.

The Prime Minister accepted that the election had been “very difficult” and there had been some “challenging results”.

Speaking at the Welsh Conservative spring conference in Llangollen, she said: “There was a simple message from yesterday's elections to both us and the Labour Party: just get on and deliver Brexit."

Later, after addressing the Scottish Conservative spring conference in Aberdeen, Mrs May stressed that she was pleased Mr Corbyn had also accepted the need for urgency to get an agreement done.

Ruth Davidson, the Scottish Tory leader, who returned to the political fray at the conference following six month’s maternity leave, said the message from the election results seemed to be a “plague on both your houses”. She hoped the results would focus the minds of those in the cross-party talks to agree a deal so the UK Government could move onto the next stage.

While the two main parties suffered a hit from a Brexit backlash in this poll, it is likely to be nothing compared to the one they could receive on May 23 in the European elections if the cross-party talks crash to failure. The expectation is that, in such a circumstance, Nigel Farage’s Brexit Party would win the poll; the pressure on Mrs May to resign at that stage could become irresistible.

But as the Conservative losses mounted up south of the border the calls for her to go increased.

Priti Patel, the leading Brexiteer and former International Development Secretary, noted: “We need change, I don’t think we can continue like this….Many of my constituents have said this to me: we need a change of leadership, perhaps the time has now come for that.”

Senior Tory Brexiteer Sir Bernard Jenkin claimed the PM had “lost the plot” and warned the party would be "toast" unless it "mends its ways pretty quickly".

At the Welsh conference, Mrs May was heckled by 71-year-old Stuart Davies, who called on her to go. Afterwards, he said: “I am furious at what she has done to our party. To put it bluntly, she is telling lies; 'We will be out by March 29'…I did what I did because I know it was the right thing to do."

There was also a warning for Mr Corbyn from within his own party’s ranks.

Remain-backing Labour MPs warned him against striking a Brexit deal without the promise of a referendum after Barry Gardiner, the Shadow Trade Secretary, suggested the party was "bailing out" the Tories in the cross-party talks.

London MP Wes Streeting said: "Labour should not be bailing the Tories out. Any deal - any - must go to a public vote. Without a commitment to a public vote, I'll vote for a Labour-Tory deal when hell freezes over and I'm not alone in that."

Meanwhile, Nicola Sturgeon issued her own caution to Mr Corbyn and his colleagues. “If the message Labour takes from English local elections is that they should now be the facilitator of a Tory Brexit, I suspect their troubles will just be beginning," said the First Minister.

As the Tories and Labour licked their wounds, there was jubilation in the Liberal Democrat and Green camps.

At a victory rally in Chelmsford in Essex, where his party seized control of the council from the Tories, Sir Vince Cable told activists: "The Lib Dems were written off at one point but we're coming back very, very strongly. We're the big winners of the night throughout the country."

He added: "Voters have sent a clear message that they no longer have confidence in the Conservatives but they are also refusing to reward Labour while the party prevaricates on the big issue of the day: Brexit.”

The Greens were also upbeat. Jonathan Bartley, the party’s co-leader, said it had been the “biggest election night in our history” and that his party’s message was “clearly taking hold and can win anywhere”.

He insisted: "Voters see that we need a new kind of politics, one that recognises the huge imperative of acting on climate change but also the social emergency that is creating misery and suffering in communities across the country."

Change UK MP Chuka Umunna said: "These local election results illustrate that people believe, as we do, that politics is broken in Britain and the two main parties are responsible, which is why our MPs left them; those parties can't be the solution because they are part of the problem."

In terms of councils, the Tories lost control of 33, including Peterborough, Basildon, Southend, Worcester, St Albans, and Folkestone and Hythe. However, the party held on in the bellwether council of Swindon, seen as a possible Labour gain, and took Walsall and North East Lincolnshire from no overall control.

Labour managed to gain control of Trafford in Greater Manchester for the first time since 2003 but forfeited control in heartland councils like Burnley, Darlington, Hartlepool and Bolsover.

The biggest winners were the Lib Dems who took more than 10 councils mainly at the expense of the Conservatives. These included Chelmsford, Winchester and Bath.