‘Aren’t the children quiet,’ says the shadow education secretary, Angela Rayner, to a group of parents at a community centre in Crewe. They have come to hear her talk about the rising cost of childcare during the summer holidays. “My children wouldn’t be that quiet!” Rayner is good in these situations; she understands the problems faced by parents trying to keep their children safe during the summer. One says he struggles to afford the £8 a day charged by a local club for his child to attend. She empathises. She is strong on empathy. You feel Jacob Rees-Mogg might find this harder.

Rayner is at the meeting with the new Labour MP, Laura Smith, who gained this seat by just 48 votes in June. Smith has brought along a gift of baby clothes for Rayner, who at 37 will become a grandmother in December when her 20-year-old son and his girlfriend have a baby. She’s going to be a “glam-ma”, she tells me later with her engaging laugh punctuating her conversation, adding: “It does qualify me as proper working-class and Jeremy Kyle.”

No one doubts that she is proper working-class, and a very unusual politician. She grew up on a council estate in Stockport; had a mother who couldn’t read or write; left school without any qualifications; got pregnant at 16 and left home to bring the child up alone (“If you’re old enough to get pregnant, you’re old enough to look after it,” her father told her). She is now the mother of three boys, one of whom was born at 23 weeks and is registered blind. That 20 years later she is on the Labour frontbench – just two years after becoming the first woman to represent Ashton-under-Lyne, in Greater Manchester – and has been tipped as a possible Labour leader is remarkable.

It would be a mistake to define her just by her background– a backstory only takes you so far in politics – but it’s hard not to dwell on the details. “I remember going round to my friends’ houses and asking them to ask their mum and dad if I could stay for dinner because I wasn’t going to get fed,” she says, matter-of-factly. “My mother suffers mental health problems and has a learning deprivation. I remember her first mental health crisis when she said she wanted to kill herself. I was 10, and I slept at the bottom of her bed to stop her. From an early age, I remember the relationship flipping. I became the parent.”

As the eldest daughter, helping to run the home fell to her. It meant she got only the sketchiest of educations. “School was the place where I hung about with my mates and got a meal. My mum didn’t understand that education was an important thing. She couldn’t do my homework with me. I was helping her read stuff. She once brought shaving soap thinking it was whipped cream.”

The transformation in Rayner’s life over the past two decades is down to her personality – “I’ve always been the girl who can’t sit on her hands. If there’s a pink elephant in the room, I’ll identify it and say it” –and her work with Unison. She became a home-help working with the elderly while still a teenager, and joined the union when Stockport council was threatening to outsource jobs, helping to fight a successful campaign to keep them in-house. She became a full-time union official when she was in her early 20s, and 10 years later, having shouldered aside a few crusty blokes she thought were underperforming, became the union’s convenor in the north-west, representing 200,000 workers.

Her relationship with the father of her first son ended quickly, but her marriage to fellow Unison official Mark Rayner – her maiden name had been Bowen – brought stability to her life. She says he has been willing to step back from his job, and do a good deal of the childcare – her younger sons are eight and nine. The day we meet started with her having an on-air row over tuition fees with Piers Morgan on Good Morning Britain and is due to end with a late-evening constituencymeeting on tower-block safety. Her time in Crewe overruns, so most of our conversation takes place as she drives me back to Ashton. This is a 14-hour working day for her, and she admits feeling “the odd pang that I’ve abandoned my children”.

Her argument with Morgan concerned tuition fees, and the confusion over Jeremy Corbyn’s pre-election interview with the NME in which he had said he would “deal with” accumulated student debt. Was it a promise or just a throwaway remark that meant nothing in practice? “If you listen to the whole interview that Jeremy gave,” Rayner says, “he recognises it [accumulated debt] is a problem, and says he’d like to do something about it, but he is quite clear that he hasn’t got a solution. There was nothing in our manifesto on back debt.” For a start, she says, what would you say to people who had already paid off their debt? “They’re going to ask ‘Where’s my rebate?’ There was never a promise from us on that.”

Rayner is, though, clear that the tuition fees system is unsustainable. “If we got in tomorrow, we would abolish tuition fees and annul the fees being paid in the current year. That would cost £9.5bn a year. We would also bring back maintenance grants, which would cost £1.7bn.” She says the very fact that debt is now more than £100bn and that much of it will never be paid off shows that it is a financial timebomb.

The other big issue swirling when we meet is Brexit. A few days before, Corbyn had insisted the UK would have to leave the single market, although that seemed to be news to his Brexit spokesman, Keir Starmer. The creative ambiguity that served Labour so well during the election was continuing. Where does she stand? “I didn’t think we should have Brexited,” she says. “However, there is absolutely no way you can disrespect the way the people voted. My constituency was very heavily in favour of leaving.” She does, though, echo her fellow Greater Manchester MP Andrew Gwynne’s view that Labour’s position on Brexit could shift if public opinion changes. “If it was a popular thing on the streets of Britain, there could be another referendum, but until the general public has a change of heart, we’re going to exit Europe.”

I suggest the catch-22 is that the public can’t make a change of heart clear without a second referendum, but there can’t be a second referendum until the public has had a change of heart. Rayner disagrees. “The public can make their feelings clear, and there can be a groundswell for it. Politicians are political animals; they’re savvy. That’s why most of them are saying they respect the vote. But MPs haven’t changed their mind on Brexit. Most of them are weeping. They want to stay in the EU because they think this is going to be really damaging. If I got a feeling in my constituency that the public wanted to remain, I’d say: ‘Brake!’”

Rayner has been loyal to Corbyn, but she does not define herself as a Corbynista and backed Andy Burnham in the 2015 leadership election: “I’m Labour through and through, and I wouldn’t define myself by a particular leader.” She is a socialist, but less ideological one than some of her colleagues. “Ideology never put food on my table,” she says. She has successfully scuppered Theresa May’s flagship policy to build a new generation of grammar schools, but doesn’t propose abolishing existing ones because that would mean destroying good schools. She makes an economic case for better education, health and social care, arguing that early intervention and proper support will save money in the long run. She even praises Blair for winning three elections. “I’ve been considered rightwing, moderate, hard left,” she says. “I see myself as soft left. I’m very pragmatic. I’m interested in how we can change lives for the better; how we can we put socialism into practice. Every time we expend energy on fighting each other, we’re letting down the people that need us the most.”

When she became shadow education secretary a year ago in the darkest days of the Corbyn leadership, she was mocked for her Mancunian accent, class, and occasional verbal slips, but she reckons she has now established herself. “I was thrown in at the deep end, and I could have sunk. But I didn’t just tread water. I was able to swim around and take command of my brief to the point where it feels like I’m the government and they’re attacking me.”

Tory blokes in the Commons still give her a hard time, and there was a dust-up over tuition fees just before the recess in which the speaker John Bercow felt obliged to intervene. But Rayner says she enjoys the boisterousness. “I grew up in a pretty rough area. I remember singing in a karaoke bar once and watching some guy get potted [hit in the face with a glass]. I was singing Waterloo and the girl who ran the karaoke just said carry on, so I’m singing Waterloo while this guy is bleeding.” Even Brexit hasn’t yet reduced parliament to that.

Her story is inspiring. “When I was pregnant at 16 I felt ashamed, I felt embarrassed. Growing up I was always made to feel I wasn’t good enough. I was called a scrubber. People said: ‘That’s it, she’s going to have loads of kids with different dads and be in a council house all her life and amount to nothing.’” She proved the cynics wrong, and made her mother very proud. “She says: ‘I watched the telly and saw you in parliament, I didn’t understand it, but you sounded good.’”

Can she ever be leader? “I don’t know if the great British public could see someone from my background leading the country,” she says. “If I were leader one day, it would be because I think that’s the best way of making a difference. I’m ambitious for that, but it’s not about me, because it puts an enormous amount of pressure on you as an individual, especially if you’re a person who feels like someone’s going to tap you on the shoulder any moment and say: ‘C’mon now, you put on a good show, but joke’s over now, off you pop.’

“I already feel like I’m punching above my gene pool. I’m in a place achieving things I never dreamed of being able to do. What gives me the confidence to do it is knowing I’m speaking up for my class, the people that I’m there to represent.”

Who knows, if the public continue to value authenticity, she may have a chance. It would certainly make a change from government by Etonians.