London (CNN) The British media landscape may be dominated by Britain's tortuous negotiations to leave the European Union, but the country's main opposition party has other ideas.

The Labour leader, Jeremy Corbyn, who has spent the past three years repositioning the party firmly to the left of the version fashioned by former Prime Minister Tony Blair, thinks voters are tired of the endless bickering over Brexit and want someone to address their day-to-day concerns.

So on Wednesday, at the party's annual conference, Corbyn sought to articulate an unashamedly socialist program that he believes will propel him to Downing Street in the event that the beleaguered government of Prime Minister Theresa May collapses.

Issuing a rallying cry to voters disillusioned by a decade of austerity since the financial crash of 2008, he called for fundamental reform of a "broken economic system" and an end to "greed-is-good" capitalism.

In his speech, Corbyn attacked the "political and corporate establishment" and a "deregulated" financial system, doubling down on a number of policies detailed in Labour's manifesto ahead of last year's general election, at which the party won 40% of the vote and denied May's Conservatives a parliamentary majority.

Labour leader Jeremy Corbyn in Liverpool during the first day of his party's annual conference.

The Labour leadership believes this message will resonate in areas of the UK that voted "Leave" in the Brexit referendum of 2016.

But a problem for Corbyn is that Labour's rank-and-file membership, which swept him into the top spot after years on the leftwing fringes of the party, are resolute supporters of Britain's membership of the European Union.

Divisions over Brexit were laid bare on Tuesday when delegates in Liverpool forced a shift in the party's position on a second referendum, voting for a policy that puts a new vote on the table in the event that May fails to get a Brexit deal through the UK Parliament.

Speaking Wednesday, Corbyn sought to play down the divisions on Brexit, saying that Labour aims "to get the best Brexit deal for jobs and living standards," a deal that would underpin the party's broader plan for fundamental economic reform.

He confirmed that Labour would oppose leaving the EU without a deal, and vote against the "Chequers" plan -- agreed by May and her cabinet in July but criticized by some EU negotiators. He added that "all options are on the table" if the government fails to negotiate a deal that Labour could support. Notably, he did not specify that a second referendum was one of those options.

Corbyn offered an olive branch to May, saying Labour would vote for a deal that kept Britain in the EU's customs union and avoided the return of border infrastructure on the Irish border. It was a politically astute move -- if May returns with such a deal after the conclusion of negotiations with the EU, it could get through Parliament with Labour votes but precipitate a damaging split inside her own party.

An end to 'greed-is-good' capitalism

The comments on Brexit came near the end of a speech that dwelt heavily on a left-wing alternative to the populism of the far right, which has dragged the political center of gravity rightwards across much of Europe.

Corbyn's program echoes the demands of socialist movements around the world, including the Democratic Socialists in the US, in his call for wealth redistribution and a fairer economic system, designed "for the many, not the few."

Over the past three days at Labour's gathering in Liverpool, a post-industrial city in northwest England hit hard by austerity, senior party figures have outlined a series of measures that, taken together, amount to nothing less than a transformation of Britain's economic and social order.

Jeremy Corbyn (L) sits with Shadow Chancellor John McDonnell following McDonnell's speech at the Labour party conference on Monday.

Labour has pledged to rejuvenate the UK's neglected high streets, nationalize public services and some major industries, and force all large firms to give their employees a share of the business and a voice on their boards. Critics of Labour say these policies are throwbacks to failed socialist governments of the 1970s. But Corbyn's top team knows they are popular with voters who believe they have been punished for the failings of reckless financiers.

"Ten years ago this month, the whole edifice of greed-is-good, deregulated financial capitalism, lauded for a generation as the only way to run a modern economy, came crashing to earth, with devastating consequences for millions of people," Corbyn said, to rousing applause from delegates.

"But instead of making essential changes to a broken economic system, the political and corporate establishment strained every sinew to bail out and prop up the system that led to the crash in the first place."

Left-wing politics alive and well?

Despite internal divisions over Brexit and accusations of antisemitism, recent polling suggests support for Labour remains steady. Voters, it seems, are not turned off by the leftward drift.

Corbyn's rise draws comparisons with the leftwing wave successfully ridden in the US by Bernie Sanders. At an event at the University of Cambridge a few days before the UK general election last June, Sanders praised the Labour leader's willingness to address issues such as wealth inequality, poverty and class.

"Too many people run away from... the grotesque levels of income and wealth inequality that exist in the United States, that exist in the UK, and exist all over the world," he said, adding that "globalization has left far too many people behind."

But while Corbyn has cemented his dominance over Labour, similar ideas have yet fully to take hold in the US Democratic Party. A turning point was perhaps the unexpected victory of Alexandria Ocasio-Cortez over 10-term incumbent Joe Crowley in a New York congressional election in June. Ocasio-Cortez is a member of the Democratic Socialists of America, a grassroots socialist movement that rose from the success of Sanders,

recent poll suggests that support in the US for a "move away from capitalism to more socialism" is higher than at any time in the last decade, suggesting that future successes could be on the cards.

And despite the undeniable growth of far-right parties across much of Europe, a number of left-wing or socialist parties have also been making gains.

The relative successes of Podemos in Spain, Syriza in Greece, Die Linke in Germany and Jean-Luc Melenchon's insurgent movement in last year's French presidential election have shown how left-wing politics can counteract the rise of the right.

Corbyn hopes the same trend can hand him the keys of 10 Downing Street if, or perhaps when, May falls.