Lisa Nandy has become the second candidate to make it on to the final ballot in the Labour leadership contest, after picking up a nomination from Chinese for Labour, on top of the endorsements she has already received from the NUM and GMB unions.

Nandy, who joins Keir Starmer in making it through the nominations process, said: “As someone of mixed heritage, I’m incredibly proud that it is Chinese for Labour who have secured my place on the ballot paper.

“They do incredibly important work to ensure we are a representative and inclusive party that can truly speak for modern Britain.

“I’m now looking forward to getting out into the country and laying out my vision for reuniting the party, rebuilding trust, and returning Labour to power at the next election.”

Under the somewhat complex leadership rules, candidates who get sufficient backing from Labour MPs and MEPs have to then be endorsed by at least three affiliates or unions, making up at least 5% of affiliated members.

In practice, the 5% threshold means candidates need to get support from at least one of the major unions if they are to get through.

Nandy, who set out her pitch for a shake-up of the welfare and social security system in a speech on Wednesday, received a boost earlier in the day after rival Jess Phillips, who quit the race, endorsed her.

“I’ve said that right now, I can’t bring the party together and that’s why I have withdrawn from the race,” said Phillips, who looked unlikely to gain the necessary support from unions or local parties to advance.

“I think both Lisa and Keir can unite the party and begin the process of winning back trust with the country,” the MP for Birmingham Yardley said. “I’ll be voting for Lisa and Keir, as I think that they can do that. Lisa will be my number one preference.”

Nandy remains a significant outsider to take over from Jeremy Corbyn, with YouGov polling showing her on 7% of Labour members’ first-preference votes, well behind Starmer, the shadow Brexit secretary, on 46%, and Rebecca Long-Bailey, the shadow business secretary and choice of the Corbyn camp.

The final person still in the race, the shadow foreign secretary, Emily Thornberry, is polling at 3% among members and struggling to acquire the necessary backing of unions and party affiliates, or local Labour parties.

Asked if her campaign was picking up speed, Nandy said she accepted that she remained a lesser-known figure to many members, but that she hoped this was changing. She added that even if she did not win, her prescription for a fundamental shift in the party would be picked up by another victor.

“Whoever wins this leadership contest, whether it’s Emily, Becky, Keir or me, what we’ve got to make sure that we do is raise the bar on our ideas,” she said.

Nandy said she hoped a woman could win: “It is painful to me that we are a party that stands for equality but we’ve never had a woman [leader]. I think we may be the only party that’s never done it.”

Speaking at the homelessness charity Centrepoint, where she worked before becoming an MP, Nandy reiterated her calls for Labour to embrace fundamental change if it was to bounce back from December’s crushing election defeat.

Expanding on comments she made on BBC Radio earlier on Wednesday, Nandy criticised the Blair and Brown governments for not pushing back against the Thatcher-era idea to end the postwar consensus on the importance of the welfare state.

“We tacitly accepted that four decades of economic conservatism was a bigger priority than people, that only by showing we could be as tight as the Tories could we buy legitimacy for helping people in the most need,” Nandy argued, saying it was only under Corbyn that Labour changed tack.

Nandy, often a critic of Corbyn, and who said the scale of promises made in the 2019 Labour manifesto was frightening for voters, said she would pay for a fairer social security system in part by taxing wealth at the same rates as income.

She also argued that companies that make a profit but fail to pay the living wage to staff should be obliged to make up the difference in higher tax bills: “I think we need to start calling this out for what it is. This is a system that allows profit to be put before people.”

Nandy said she would also scrap universal credit and replace it with a benefits system that reflects the “complexity and the lived reality of the people in it”.