Momentum’s alternative Labour conference, the World Transformed, is back in Liverpool, where it was born two years ago. And like the city’s most famous sons, the Beatles, the grassroots group has ambitions to make it big in the US, where socialism is the new political buzzword.

At TWT one of the star turns has been Julia Salazar, the charismatic activist who this month defeated a veteran incumbent in a Democratic primary to run for a seat in the New York state senate.

Momentum is keen to develop its connections with US movements, swapping campaigning ideas and forging connections. Salazar said the group had a growing reputation among newly enthused socialists across the Atlantic.

“Momentum has influenced a contingency within the Democratic Socialists of America, we’ve followed it for quite some time,” she said. “There are real parallels with the leftward shift in Labour and the insurgence and resurgence of socialists in the Democratic party.

“And there are also parallels with the resistance – there are lot more mainstream, liberal Democrats who are very resistant to the entry of leftists and socialists like myself into the party. They see us as the existential threat to centrism.”

Salazar, who was born in Florida to a conservative immigrant family, said her political awakening came during her college years and her time working as a nanny and cleaner.

Julia Salazar speaks to supporters before a rally in Brooklyn last month. Photograph: Mary Altaffer/AP

“I think the platform of a democratic socialist appeals … to someone who might have reactionary politics but who also recognises their class interest and self-interest is more aligned with a democratic socialist vision than a conservative one,” she said.

She said US Democrats could learn lessons from some of the successes of Labour’s 2017 general election campaign. “It’s a myth that it’s safer for Democrats or Labour to run candidates that capitulate to the centre,” she said. “It’s riskier because it is uninspiring, so fewer people are going to come out to vote.”

Many of the US speakers at the World Transformed, including the politician Lee Carter and Bernie Sanders’ former adviser Becky Bond, pointed to the parallels between Brexit and the election of Donald Trump, and the simultaneous growth in interest in leftwing politics.

Links between leftwing US political activists and Momentum have been growing for years. Adam Klug, one of Momentum’s co-founders, now works in the US on progressive campaigning for the Social Practice, a consultancy founded by two Sanders campaign veterans.

Klug said British and US campaigners had adopted methods from one another, both in the UK general election and in multiple elections across America.

Campaigners in the US have adapted Momentum’s “unseat” campaigns, which in the UK have targeted high-profile opposition politicians such as Iain Duncan Smith and Boris Johnson, with campaigners attending rallies then going out on mass door-knocking sessions.

The Real Justice PAC, which promotes progressive candidates for elections of public prosecutors, has since held similar sessions, fronted by another prominent campaigning journalist, Shaun King.

In turn, Momentum has taken on many of Sanders’ campaign tactics, including pop-up phone bank parties and “persuasive conversation” training.

The Momentum version of that training was developed during the general election campaign and it has since passed it on to the US National Nurses United (NNU) for use in its Medicare for All campaign.

Bonnie Castillo, the executive director of the NNU, one of the country’s biggest and most politically outspoken unions, said making international connections was hugely important to the movement, especially making the case against privatised healthcare.

Momentum members are due to take part in phone banksessions to contact US voters, to make the case in favour of nationalised healthcare and the NHS as part of the NNU’s campaigning.

Castillo, who spoke at the World Transformed, said she was inspired by the concept of a leftwing grassroots festival running alongside a mainstream party conference.

“We share common vision and this is an incredible space here, and we have not done this yet, but we could and we can,” she told the crowd at the World Transformed, to huge applause. “And when we do, it will be international and we will invite you all!”