Anthony Albanese and the British prime minister, Keir Starmer, have warned progressive governments must keep faith with voters on economic and immigration policies to effectively marginalise the political far right.

Visiting London for talks with UK Labour and progressive leaders from Canada, Spain and Iceland, the prime minister said careful management of Australia’s borders was key to maintaining support for legal migration and mainstream political parties, as well as delivering real wage growth for workers.

Despite Starmer declaring the UK Conservatives “dead” as a political force, Albanese met the party’s leader, Kemi Badenoch, but said he would not make time for the leader of Reform UK, Nigel Farage.

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The anti-immigration party has almost double-digit leads in major polls in recent weeks, dragging support from the Conservatives.

“People are concerned about elements of the far right rising in various countries,” Albanese said after talks at 10 Downing Street.

“What our job is to do is to make sure that people continue to have faith in the system. That’s something that my government’s very focused on.

“I don’t want to see the rise of populist organisations such as [Reform]. I met with the mainstream opposition party here. Parties of governance have to come up with solutions, not seek to divide people.”

Albanese said delivering on Labor’s 2022 and 2025 election promises was critical to voters support.

“We have kept Operation Sovereign Borders [the Abbott-era policy to stop migrant boats]. We’ve continued to maintain a strong control of our borders. We have turned back boats.

“We’ve done things that we said we would do, and that’s been important to ensure that you can have that faith from people that you’re prepared to undertake an orderly system.”

Starmer went further, using a speech to the Global Progress Action summit in London on Friday to call on progressive politicians to push back against lies by populists, to undercut an “industrialised infrastructure of grievance”.

“It is now time for social democrats to confront directly some of the challenges and some of the lies, frankly, that have taken root in our societies.

“Because we don’t just hear these stories about our politics, we also hear stories about our great countries, our communities, our cities, that simply do not match the reality that we see around us.”

He called for a “patriotic renewal” in politics, echoing Albanese’s rhetoric of “progressive patriotism”.

Starmer also pushed back on criticism of London by the US president, Donald Trump, including attacks on the mayor, Sadiq Khan, and claims Muslims were seeking the introduction of sharia law.

“You may have noticed that this city isn’t the wasteland of anarchy that some would have you believe,” he told the conference.

Canada’s prime minister, Mark Carney, and Iceland’s Kristrún Frostadóttir appeared at the conference, stressing strong economic policies was critical to support for mainstream parties.

Albanese also met the Spanish prime minister, Pedro Sanchez, on his first full day in London before a visit to Balmoral to meet King Charles on Saturday, and attending the UK Labour conference in Liverpool on Sunday.

On his meeting with Starmer, Albanese said the pair had discussed the Aukus nuclear submarines agreement with the United States, before the completion of a review being led by the Pentagon.

Albanese will discuss the nearly $400bn plan with Trump at the White House next month.

“There is no indication that I’ve seen of anything other than support for Aukus going forward,” he said. “It is in the interests of all three nations.”