Britain’s new prime minister has sometimes seemed to be everywhere all at once in his first two weeks in office.

A morning visit to a London homeless shelter. A meeting with President Volodymyr Zelensky of Ukraine at a military base. A speech at a Jewish care center.

He has been ubiquitous online, too, posting dozens of direct-to-camera videos on TikTok, X and Instagram. He poured a pint at a local pub, wore a construction worker’s orange vest to talk about youth unemployment and stirred up a lighthearted controversy over the proper way to make a cup of tea.

It may look frenzied, but Prime Minister Andy Burnham’s message is focused: I’m for you, not them.

The former mayor of Greater Manchester, Mr. Burnham has already announced lower taxes on pubs, pledged reform of social care programs for the disabled and the elderly and found some money to lower electric bills. He has capped bus fares at 2 pounds (about $2.69), vowed to help young people get jobs, promised to end homelessness and said he would shift power and money away from London to regional mayors and municipal leaders.

“The electorate’s been really clear: It wants change,” said Paul Dennett, who served as Mr. Burnham’s deputy in Greater Manchester and is the mayor of Salford, a nearby city. “I think Andy fundamentally gets that.”

It is far from clear where all the money is going to come from. Rivals have warned that Mr. Burnham’s promises will most likely entail either higher taxes or higher government borrowing. And he is pushing some painful decisions about trade-offs down the road: The shape of his promised overhaul of the social care system, for example, will not be clear until next year at the earliest, once a review has been completed.

Still, the flurry of announcements is designed to reset the narrative at a moment when Britain’s political system has been mired in instability and ideological churn. Mr. Burnham, who represents the center-left Labour Party, is the seventh prime minister in a decade. The turnover has left many Britons disillusioned with politics.

In a video shared by news networks last week, an elderly man at the Jewish care center is introduced to Mr. Burnham. “You are the local candidate, are you?” the man asks. Mr. Burnham laughs and explains that he is the prime minister. The man responds with incredulity: “What, a new one? But they keep changing every five minutes.”

Mr. Burnham is well aware. His Labour Party predecessor, Keir Starmer, lasted only two years and 15 days. Rishi Sunak, a Conservative, never made it to the end of his second year. And Liz Truss lasted only 49 days.

To avoid a similar fate, Mr. Burnham has taken a page from President Trump’s political playbook — starting his term with a shock-and-awe burst of policies. He has also learned from Mr. Starmer that first impressions matter. In 2024, after leading Labour to victory, Mr. Starmer made a series of political missteps and stumbles that were pounced on by Britain’s tabloid newspapers.

Mr. Burnham often posts hand-held videos of himself talking directly to camera. In one, he weighs in on a contested issue in Britain: whether to put milk in a cup of tea before or after the tea bag steeps in hot water. When he admitted putting the milk in first, some parts of the internet exploded in outrage. (In a later video, he made fun of himself by hinting that he was watching videos on how to make tea the right way.)

He is also spending one day a week working from his new “No. 10 North,” a nondescript building in downtown Manchester, to demonstrate his argument that decision-making shouldn’t happen only in the hallowed halls of the national government in London.

Rob Ford, a professor of politics at the University of Manchester, said Mr. Burnham is much better than Mr. Starmer was at capturing the public’s mood.

In his speech about Britain’s faltering system of caring for the elderly and the disabled, the prime minister said it was “as unfair as American health care,” a reference to what many British people think about the system in the United States. Later he pledged to create a “National Care Service” similar to the National Health Service in England. On education, Mr. Burnham has promised to “value the hard hat as much as the graduation cap.”

“He understands about symbolism and narrative,” Mr. Ford said, comparing him to former President Bill Clinton.

The new prime minister also speaks about his own life. He has talked openly about his father, who has Alzheimer’s and lives in a nursing home. “I’ve just got to speak from the heart when it comes to this issue,” he said in his social care speech, “because it is very, very personal for me right now and for my family.”

It’s early, but so far Mr. Burnham’s approach seems to be working. Recent polling indicates that his personal popularity is strong, and the Labour Party has overtaken or leveled with its populist right wing rival, Reform U.K., in several polls.

But Mr. Burnham is just getting started, and there will be tests of his mettle ahead.

The war in Iran could increase prices for energy just as winter arrives this year, raising the cost of living.

When Mr. Burnham said that he was determined to tackle the long-running social care crisis in Britain, The Daily Mail, a conservative tabloid, splashed its front page with the headline: “BURNHAM’S £18 BILLION ‘DEATH TAX’ NIGHTMARE.”

That was a not-so-subtle reference to a proposal Mr. Burnham embraced when he was a young health secretary in 2010, for a tax on estates to fund social care. The Conservative Party at the time branded it a “death tax.” The prime minister will have to withstand those kinds of political attacks if he wants to push through his agenda.

He will also have to navigate criticism from both the right and the left on contentious issues like immigration. Shabana Mahmood, who has remained home secretary in Mr. Burnham’s government, has proposed a crackdown on asylum seekers and other changes that will make it tougher for immigrants to stay in the country indefinitely. That has already drawn intense opposition from some left-leaning Labour lawmakers.

Rivals on the right, including Nigel Farage, the head of Reform U.K., accused the prime minister of ignoring the topic during his busy first weeks. On Sunday, Mr. Burnham visited the white cliffs of Dover where he was briefed by the Coast Guard on the issue of migrants trying to cross the English Channel in small boats.

Of course, he made a video.

Mr. Dennett, the mayor of Salford, said Mr. Burnham was making deliberate decisions about how to use his time and his voice.

“People are often criticizing politicians for not tangibly improving things in terms of the material conditions of their lives,” he said. “What we have in Andy is someone who’s both pragmatic, but also strategic.”