Andy Burnham, who was installed on Friday as the leader of Britain’s Labour Party, is almost at the end of his long journey to Downing Street.

On Monday, he will take the final step, when King Charles III asks him to form a new government and become the country’s 59th prime minister.

It will be the culmination of a quarter-century in elected politics in which Mr. Burnham served in Parliament, twice failed to become Labour leader, left to run one of Britain’s largest cities and finally returned to Westminster, a place he long railed against as detached from the struggles of the working class.

In remarks to a special Labour Party conference in central London, Mr. Burnham called for having “the courage to fix the big things that politics has neglected” and pledged to “challenge a political culture and an economic model that simply doesn’t work well enough for ordinary people.”

That will be no small task. The former mayor of Greater Manchester will take over from outgoing Prime Minister Keir Starmer at a time of political upheaval and economic stagnation in the country that has churned through seven prime ministers in the last decade.

When he walks into No. 10 Downing Street next week, Mr. Burnham will face many of the same structural problems that have bedeviled his predecessors: slow growth, high government debt, a struggling health service and political fissures. In his remarks, Mr. Burnham seized on a word that helped previous politicians, including former President Barack Obama: hope.

“We are united and we put the power that comes from that unity at the service of people and places who have been waiting too long for politics to let them hope again,” he said. “That’s what we are going to do, everybody. We are going to give them hope back.”

Mr. Burnham’s skeptics question whether he has the mettle to make tough decisions. Joshi Herrmann, a British journalist and founder of the Manchester Mill newsletter, who has covered Mr. Burnham for years, said he lacks the “almost slightly inhuman, cold blooded steeliness” of former Prime Minister Tony Blair.

And he argues that as a lawmaker and then mayor of Greater Manchester, the region that surrounds one of Britain’s largest cities, Mr. Burnham demonstrated a chameleon-like quality that allowed him to appeal to many different groups. “I mean, spoiler alert: he doesn’t have a political philosophy,” Mr. Herrmann said.

In his speech on Friday, the soon-to-be British leader confronted that critique directly. He referenced a well-known joke often made at his expense that plays with the idea that he served under three Labour leaders with different political ideologies — Tony Blair, Gordon Brown and Jeremy Corbyn.

“A Blairite, a Brownite and a Corbynite walk into a bar,” the joke goes. “The bartender looks up, sighs and asks: ‘What’ll it be, Andy?’”

Mr. Burnham smilingly turned the joke on its head, calling unity an essential part of repairing the Labour party. “In future, when a Burnhamite walks into a bar, I want the barman to say: ‘Great to see you — we don’t like factional politics in here,’” he said.

His short speech on Friday was the beginning of what is likely to be a concerted effort to prove his doubters wrong. In it, he reassured the audience that “I know what I believe after 25 years as an elected Labour representative. And I know what I want to do. I have a plan.”

But he offered few details about what the plan includes. He talked about building a government that will “speak for all parts of the country” and handing power back to local communities, and said he would be a pro-business prime minister. At the same time, he said his government would be a “distinctively Labour” one.

“People are looking for us to deliver,” he said, “and we will.”

To deliver, Mr. Burnham will have to avoid the bruising intraparty fights that helped drive his predecessor out of office. Mr. Starmer repeatedly clashed with progressive members of his party. When he resisted their guidance, they rebelled. When he caved to their pressure, his critics accused him of not having a backbone.

Mr. Burnham hinted that more detail will be forthcoming soon. Amid days of speculation about his choices of cabinet ministers, the incoming prime minister said he had not made any final decisions.

“But I will soon,” he said. “And when I have, you will see it reflects all parts of our party, all communities. And it will reflect your own place within this great party of ours.”

Mr. Burnham’s message also contained a populist appeal as he described the need to counter the “new right” in Britain. That was likely a reference to Reform U.K., the populist right-wing party led by Nigel Farage that has led opinion polls, with about 25 percent of voter support, for more than a year.

“This country does not work for working class communities like the city of my birth,” Mr. Burnham said. “In fact, it’s worse. It turned its back on them. Political power was used viciously against them to protect vested interests,” he added, in a reference to the coverup over the Hillsborough soccer disaster, which he worked to expose.

In his career as mayor of Greater Manchester, Mr. Burnham repeatedly argued that the national government in Westminster was ignoring the needs of local communities, especially in the north of England. He has promised to set up an office in Manchester as a symbol of the government’s determination to ensure that changes.

“Britain took a series of wrong turns in the 1980s,” he said Friday, referring to the transformative but contentious government of Prime Minister Margaret Thatcher, which oversaw extensive privatization and deregulation.

One of the earliest tests for Mr. Burnham as prime minister will be how to spark growth and revive the sluggish parts of the British economy. His stated plan — “Good growth in every British postcode” — is likely to be harder to achieve than it sounds.

“The country surrendered control of the essentials — housing, water, energy, transport — and left people exposed to higher costs,” he said. “That, in turn, led to the concentration of more wealth and power in the hands of fewer people and fewer places. Large parts of Britain were deindustrialized.”

His criticism of past governments implicitly included his own Labour Party, as he said that “this generation of politicians, myself included, have failed” the people of Britain. He promised that his administration would embark on “a new path to the one we’ve been on for the last 40 years.”

Mr. Burnham will not actually be prime minister for another few days. First Mr. Starmer must go to see King Charles III on Monday to officially resign. That will be followed quickly by a visit to Buckingham Palace by Mr. Burnham, where the king will request that he form a government.

And then the hard work begins.