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 likely entail either higher taxes or higher government borrowing. And he is pushing some painful decisions 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.