The band members trip out of the studio, one by one, in a jumble of facial hair and hugs and bicycles. “There’s 10 of us,” says Charlotte Church, waiting by the door for her partner, musician Johnny Powell, shouting to him to hurry up. We walk to Church’s car. Powell and one of their other bandmates sit in the back and for the next half an hour, they talk about music (R Kelly is a band favourite, “but it’s problematic,” says Church, “because he’s so fucking immoral”), slag off the charts, but mostly skip through favourite or forgotten R&B tracks that Powell pumps through the stereo. We drive out of Cardiff with Church singing every word.

It feels like a rush-hour version of Late Night Pop Dungeon, Church’s music collective that became the fringe hit on last year’s festival circuit. The band sing covers – from Bowie to Beyoncé to Aretha Franklin to Nine Inch Nails – but it’s not karaoke. The songs are twisted and looped and mixed together, miraculously uniting in what Church describes as “a release. It’s like a pressure valve for the audience, but it’s also a big warm hug.”

They were the hit of last year’s alternative All Tomorrow’s Parties festival; they perform at this weekend’s Pride in Birmingham and at Where Are We Now? in Hull next weekend.

We arrive in Church’s village, and the others get out of the car, to go and pick up her two children from an after-school club, and Church and I head to the pub. She is pregnant with her third child, and says she’s sorry if she doesn’t make sense. “My brain is just like…” She makes a “bleugh” sound. But she is articulate, sharp and funny. She loves the alternative route her music career is taking. Is it fair to say she is starting to gain the credibility she once lacked? “Totally. Absolutely. And I think I stopped worrying.” She used to try so hard before, she says. Now, she feels freer to try new things, more – as she puts it – willing to say: “Ah, fuck it.”

Church, 31, has been famous for nearly all her life. The cautionary tabloid narrative is well-worn, and like most fairy stories it contains not a little misogyny. She became famous at 11 as the little girl who could sing arias, the “Voice of an Angel”. She soon became public property – one website ran a countdown to her 16th birthday when she would be “legal”, and Chris Moyles, then in his late 20s and Radio 1’s breakfast DJ, said he wanted to “lead her through the forest of sexuality now that she had reached 16”. She was shamed for her binge-drinking, her choice of boyfriends, her size, for being a “chav”, for being “gobby”. And, perhaps worst of all, she wasn’t grateful to the powerful men who had put her there. She sacked her manager, and she has said before that, when she was 17, Piers Morgan (more of him later) told her to stop complaining about the tabloid intrusion and just be thankful that they had made her a star.

But “intrusion” doesn’t really cover what Church had been going through. At the Leveson inquiry she described how photographers had installed secret cameras outside her home to track her movements, followed her car, and tried to take upskirt shots. Her first pregnancy was revealed in the Sun before she had even told her parents; her mother’s mental health crisis and suicide attempt were exposed by the News of the World. Both, she said, were as a result of phone hacking (she later accepted £600,000 in damages).

Church seems to have emerged from it all relatively unscathed. “I always had a good sense of what was important. My coping mechanisms, my natural defences, have just been great.” She laughs. “But also that absolutely pig-headed belief in myself. And even if it wasn’t really true, I would still behave like it and say it to myself, and then it becomes true.”

She loves her life now. She has her band, and what sounds like a settled home life – she and Powell have been together for about seven years and their first child together is due in November.

What is their day-to-day life like? “It depends. Sometimes I might be rehearsing.” Her two children with her former partner, the Welsh rugby player Gavin Henson, are home-schooled, “so sometimes I teach them, though not very regularly.” She likes to clean: “My house is spotless. I love jet-washing.There are members of my family who are ill at the moment so generally I’m running around. We’ve got two dogs. We travel. And we just try to have lots of fun.” She says she feels “brilliant” at the prospect of having another baby, although she did miss drinking at first. “And now it’s great, it’s lovely. I don’t know if I’ll ever be a party girl again.” She was 21 when her eldest child was born. “It feels very different this time around.”

It was Leveson that turned Church political. “I hadn’t been interested in politics before because I thought it was all bullshit and they were all full of bullshit. And then when I started to understand how corrupt things were in the press, in government … There was so much injustice that I was like, ‘No, I’m going to get involved and try and understand.’” She immersed herself in books, but mostly in arguments with others, “just to try and understand what people thought, why they thought it.”

Her previous impression of politicians was to take them at “face value”, she laughs. “Blair helped my mum down the stairs with a suitcase. So we were both like, ‘Wasn’t Tony Blair lovely?’ Just for that.” She didn’t like Bush. “He was very cold, he had strange eyes. And he asked me which state Wales was in, which was really stupid.”

The second time she met Blair was when he invited her and Henson to one of his last dinners at Chequers, “which was very odd. Mainly because it was like, ‘I don’t know why I’m here.’ There was the head of the SAS, all sorts of important people – and then me and Gav”.

She voted for the first time in the 2015 general election. After the Tories won, she went on an anti-austerity march, and has appeared at political events and on BBC’s Question Time. She is a fan of Jeremy Corbyn. “He’s been really level-headed, relentlessly rational, and the press are obviously gunning for him.”

She describes the bombing of a pop concert largely attended by teenage girls, as “pretty misogynistic. Just heinous. Horrific. But surely the conversation is: how do you stop it? I’ve read so much about everything the Muslim community has been doing, whether it’s spreading pamphlets throughout mosques, family members dobbing in other family members. White British people need to look at what they can do to help integrate people better. I don’t see any other way of this working.”

Charlotte Church performing with Late Night Pop Dungeon in Leeds. Photograph: Andrew Benge/Redferns

The day after the bombing, Church got involved in a Twitter spat with Piers Morgan, after she pulled him up for saying Muslims could do more to help police and MI5 “root out radicalised members of their communities”.

“By your logic,” Church replied, “men should do more to root out rapists. Doesn’t really work like that does it?” Morgan replied that he couldn’t deal with Church’s “virtue-signalling ignorance”.

There are people on Twitter not worth arguing with, says Church – Katie Hopkins is one (“a horror”). But Morgan, she says, “is a bit more insidious. Because he’s a smart man, there’s something a bit more dangerous … And also he’s really fucking establishment. He’s got a lot of power, and when he says ill-conceived, stupid shit, he needs to be pulled up.”

Just then, Powell arrives with her two children. Her daughter comes over for a hug and then they all sit at the other end of the table, chattering about their day and what to have for dinner.

Church spends a lot of time arguing with people on Twitter. Why bother? “Because I’ve had some really good conversations. I don’t know if it’s always been like this for every generation – that the current time feels the worst – but I’ve never seen things be so divided. It’s not 15 different opinions, quite often it’s two very different opinions.”

She puts the rise of the “alt-right” down to their mastery of the message. The things they say are “easy to follow, easy to believe in. It’s about the death of nuance and the fact that everybody’s opinion is apparently equal, because that’s democracy.” She believes that one of the left’s problems is that it doesn’t have this. “Because life isn’t black and white, there is nuance and grey areas in almost everything.” She is interested in the idea that the right has used shadowy companies that utilise technology and big data to manipulate elections. “It sounds so conspiracy-theory it’s ridiculous,” she says. “Are [the left] willing to use those tactics? How do you fight that? I don’t think you can.”

Marching against Tory cuts in London in 2015. Photograph: Zak Kaczmarek/Getty Images

These days, the abuse she gets is “water off a duck’s back. I’ve dealt with far worse in my time.” Will she ever stand for parliament? “Maybe when I’m older. Not now. I think it should be a calling. At the moment it’s a career path for a lot of people and I don’t think it should be that. I think there should be a system like jury service where everybody has to have a go.”

In 2015, the Welsh Conservatives called Church a “champagne socialist” – she prefers prosecco, she replied. But can you be as wealthy as she is (reports have put her worth at upwards of £10m) and be a socialist? “I’ve given money away all my life and I will continue to. I’ve always paid my tax, I haven’t moved away. I’m wealthy. But I’m not obscenely wealthy. I think you can have a good amount of savings that can see you right for the rest of your life, but these guys …” She points to her children, by now looking bored and hungry … “We should all pay inheritance tax.”

Music is still Church’s main occupation. She’s planning to release an album next year – her first in eight years. She wants it to be “really female, really healing.” And angry? “Yeah. The whole range. I’m all the emotions the majority of the time, and anger is definitely one of those, and it should come through, it’s important, and often it’s seen as unbecoming.”

Does she still feel she has something to prove? She is quiet for a while – a rare moment, I realise. “Yeah. I want to smash out a cracking album because I don’t think I’ve done that yet. I’d really like to produce something which is absolutely cohesive and stand-alone.” Does that mean she wants critical and commercial success? “No,” she says, smiling, “neither. I just want something that is undeniably brilliant, and nobody else has to think it is.”

Where Are We Now? Hull, 2-4 June.