Rebecca Long-Bailey has expanded on her aim to replace the House of Lords, saying she would instead have an elected senate, based outside of London, if she were to win the Labour leadership and then a general election.

On Friday night, launching her bid for Labour leader, in front of a crowd of about 200 people at the Science and Industry Museum in Manchester, she was welcomed with a rendition of “Oh Rebecca Long-Bailey” – similar to the chant used by supporters of Jeremy Corbyn.

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As she took to the stage in front of the packed hall, with many people standing at the back, Long-Bailey joked: “Hey guys, you’re going to have to think of a new song, you know? No pressure!”

Long-Bailey, who is one of the favourites to succeed Corbyn, said she would devolve power out of the grips of Westminster, once and for all ending the “gentlemen’s club of politics”. Going further, she said she would “sweep away the House of Lords”.

Addressing her plans for an elected senate outside of London, she said it “would have a new democratic legitimacy and should have new powers to reflect that. In my view, this should include holding the government to account on the impact of new legislation on our wealth, our wellbeing, and our environmental sustainability. And we should look at ways to ensure it is representative, with a proportional voting system for elections with a voice for all regions and nations of the UK.”

Long-Bailey also pledged to fight climate change, investing in low-carbon industries as well as “rewilding” parts of the UK.

“I will fight for a Green New Deal that ushers in a new era of prosperity, security and wellbeing. I will fight for investment in the low-carbon industries of today and tomorrow to secure a liveable planet for future generations and bring new jobs and prosperity to all regions and countries of the United Kingdom.

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“I will fight for the rewilding and restoration of our landscapes, which will multiply many times over the natural wealth that belongs to us all.”

Long-Bailey also talked about her working-class upbringing in Old Trafford and joked that her younger self would never have believed that she would one day be in the race to become the leader of the Labour party.

“If someone had told me 30 years ago when I first came here [to the museum], that I’d be back in 2020, stood on a podium, running to be leader of the Labour party, I’d have thought they must have just stumbled out of the Hacienda.

“You see I grew up in a working-class family in Old Trafford less than two miles down the road. One of five sisters, I learnt my politics sitting at the top of the stairs, listening to my dad talking about pay disputes, the union and redundancies.

“I learned my politics working in a pawn shop – that was after 18 years of Tory rule – and my God you could see what it really means when the government washes its hands of its people, when it talks about “living within our means” and rather than invest, loads debt on to the backs of the poorest.”

Long-Bailey came under fire earlier this week for her views on abortion when comments she made during the general election resurfaced. She said that she “did not agree” with the law that allows terminations on grounds of disability after 24 weeks but went on to stress that this was a personal view.

Long-Bailey did not mention the subject in her launch speech but in an earlier interview the Salford MP said she disagreed with many of the teachings of the Catholic faith.

She told ITV News: “I pray to God every day, yes, that’s just the thing I do. In terms of how faith shapes my politics, it’s my view that we have to have a society that loves each other and looks after each other.

“But my politics go way beyond my faith, and I disagree with many of the things, that certainly my church, the Catholic church, do.”