LIVERPOOL, England — As Prime Minister Theresa May struggles to strike a deal for Britain to leave the European Union without wreaking havoc on the country’s economy, her Conservative Party faces another looming threat — the popularity of the opposition Labour Party and its leader, Jeremy Corbyn.

At the close of the annual Labour Party conference Wednesday, Corbyn gave what his critics in the British press called the best speech of his 30-year career, laying out a populist vision for the softer, socialist Britain that Labour plans to offer if May is toppled over her “Tory Brexit.”

“We represent the new common sense of our time,” Corbyn declared as he proposed to “rebuild Britain” with a “green jobs revolution,” with hundreds of thousands of workers paid to erect solar panels and wind turbines to slash greenhouse gas emissions and put the country in the vanguard of the fight against climate change. He promised a United Kingdom where child care is free, railroads and utilities are re-nationalized, employees sit on corporate boards and share profits, and owners of second homes pay $4,000 a year in extra taxes.

May’s Conservatives are preparing to stage their own party conference this week in Birmingham, and her foes within the party are planning to hit hard against their leader’s compromise proposals for Brexit, the so-called “Chequers plan,” named after the prime minister’s official countryside manor where the deal was approved by her cabinet in July — approved without much enthusiasm, as Britain quickly learned. Decrying her Chequers proposals as a meek capitulation to Brussels, May’s Brexit secretary, David Davis, immediately resigned, followed by her foreign secretary, Boris Johnson, who compared her plan to a pile of excrement.

Johnson on Friday published his own Brexit scheme, which he calls “Super Canada,” based upon the trade deal recently struck between Canada and the European Union. That agreement took years to hammer out.

Some Tories were quick to support the idea, while others called Johnson’s proposals dead on arrival.

May, meanwhile, has been appealing to European leaders to back her exit strategy, but so far she has failed. European Council President Donald Tusk dismissed it as unworkable. May responded by warning Europe it is either her deal or the dreaded no-deal option — and this imbroglio has opened the door to Labour (and driven the pound sterling down).

At the Labour Party conference, there were motions and standing ovations for a second referendum on Brexit. Corbyn also said he would back May on Brexit if she meets Labour’s criteria, but that is doubtful, as those tests include the demand that any deal deliver the “exact same benefits” as Britain currently enjoys as a member of the E.U. single market and customs union. May has promised to leave both.

Shadow chancellor John McDonnell, Labour’s second-ranking leader, told delegates that “the greater the mess we inherit, the more radical we have to be, the greater the need for change.”

“It’s time to shift the balance of power in our country,” McDonnell said. “It’s time to give people back control over their lives.”

After hearing Corbyn’s speech, Tim Montgomerie, a former Tory activist who is now a blogger and columnist, tweeted, “Don’t agree with it but Corbyn has a comprehensive and maybe compelling vision for post-crash future of Britain. May doesn’t and that leaves Tories very vulnerable.”

Tim Bale, a professor of politics at Queen Mary University of London, attended the Labour conference as an observer. He said the party “put on a good show” and offered proposals that could resonate with a lot of voters.

“It captures the public mood,” as Labour tries to sound “not too radical, not too out of line,” he said.

“It makes the Tories have a think, that maybe they just can’t be absolutely sure they can beat Labour,” Bale said.

Polls ahead of the conference showed Labour and Conservatives within a few points of each other, even after a long summer that saw Corbyn and his party accused by Jewish community leaders of condoning anti-Semitism.

Corbyn traveled to Brussels on Thursday to meet with E.U. Brexit negotiator Michel Barnier and Martin Selmayr, the secretary general of the European Commission, who is in charge of no-deal planning.

“Crashing out of Europe with no deal risks being a national disaster,” Corbyn warned. “That is why I’m meeting E.U. officials today, and I will be urging them to do all they can to avoid a ‘no-deal’ outcome, which would be so damaging to jobs and living standards in both the U.K. and E.U. countries.”

The Labour Party has undergone a transformation since the election of Corbyn as its leader three years ago. Under Corbyn, Labour denied May a majority government and came within two percentage points of beating the Conservatives in the snap election in 2017. 

Many members of the Labour center — the moderate holdovers from the days of former Labour leader and prime minister Tony Blair — have been pushed aside as a more assertive left wing coalesced around Corbyn, who was once dismissed as a fringe figure.

“The party has swung to the left. We are the party now,” said June Simmons, 74, a retired marketing manager and a Labour delegate from Essex who applauded Corbyn’s speech.

Asked why the 69-year-old former backbencher representing North London was so popular among the activists, Simmons said, “Because Corbyn’s a socialist! Through and through. He’s the real McCoy.” She said she’s waited all her life for such a leader.

Daniel Metcalf, a 23-year-old web designer and Labour delegate, said he joined the party because of Corbyn and his democratic socialist vision. “The people don’t want communism, but they do want their fair share, and that’s what Jeremy Corbyn is all about.”