ONE of Sophie Walker's most vivid childhood memories is of being trapped in a shoe shop as a pitched battle between rival football fans raged on Sauchiehall Street. "I was maybe eight or nine. I was there with my mum and the staff closed up and hustled everyone upstairs," she says. "We looked down on these men beating each other and breaking windows. Another time I remember seeing an Orange march and there was a lot of jeering and threatening behaviour."

Walker, a feminist activist and former leader of the Women's Equality Party, was brought up in Glasgow after her parents moved there from the north of England when she was just six weeks old. While she loved the city, she has no doubt its macho culture influenced her perception of the world.

"Sectarianism is not an exclusively male thing and Glasgow is not the only city so divided, “ she says. “But I do remember feeling those tensions and being aware the loud voices were aggressively male.”

Luckily, there were other, more positive influences. And other, less tribal marches. Walker's mum and dad, Lesley and David were activists in the early 1970s. Angry about social injustice, they combined placard-wielding with practical action.

"I was always aware as a child of how frustrating my mother found the limits the world set on women, particularly expectations around child care and restrictions on reproductive rights," says Walker. "She and her friends opened a pro-choice advice centre that was aggressively picketed by anti-abortion activists. "

David, meanwhile, was a supportive figure, countering those aggressive male voices and proving men can be powerful feminist allies. He went out canvassing in the 2017 General Election when his daughter stood against filibuster Phil [Philip Davies, Conservative MP for Shipley] who had tried to block the domestic violence bill.

With this upbringing, Walker's future as an activist seems fated. As a child, she pressed flowers into the fence at Faslane; as an adult she fought to become Lord Mayor of London. "I always had a sense from my parents that you don't just sit down and accept the world," she says. "You embrace the best bits wholeheartedly and really challenge the bits that are unfair."

Walker is talking to me in advance of the publication of her new book Five Rules For Rebellion and her appearance at Glasgow's Aye Right festival. The book is a manifesto, a call to arms and a reminder - at a time of increasing tribalism - that activism and leadership doesn't have to be a series of pitched battles; it can be a collaborative, enriching experience.

Less a polemic than a pep talk, it is an antidote to the rising tide of despair. Walker understands what it is like to feel so angry you can hardly breathe, and how that anger can be turned inwards as self-loathing and depression. She encourages activists to marshal it; to turn it outwards into action.

Her own anger was partly kindled by her experiences of discrimination. When she started out at Reuters, she saw female reporters, but very few women in senior roles. "When I had my first child I realised what was happening," she says. "The men were largely unhampered by child care. They would go off on international assignments and their wives and their children would follow them, but very few women were able to take husbands to look after their children while they ran the Egypt bureau.”

Aren't high-profile equal pay victories - such as those at Glasgow City Council and the BBC - testament to progress? "Yes, but it is usually women taking risks," she answers. "I'd like to see movement from people who don't have to take risks. I'd like to see more understanding from the men who still disproportionately make the hiring decisions."

Walker's journey into activism - and then, in 2015, to leadership of the newly-formed WEP- was born of her five-year fight to gain a diagnosis and support for her daughter Grace , who is autistic.

Walker is a very polished - almost too polished – speaker. She is used to talking about her activism on a public stage, and so delivers her razor-sharp feminist analysis with a composure that borders on clinical. But not when she is talking about Grace. When she is talking about Grace, her rage seeps through the cracks like molten lava .

She says she discovered autism - which is said to affect more boys than girls - is seen through a male prism. "Simon Baron-Cohen described it as an extreme male brain and set the template for this extremely stereotyped idea of autism," she says. "We don't understand the experiences of women and girls on the autism spectrum because we don't do research."

For some of those years, Walker was a single mother. She went part-time in order to devote time and energy to fighting for her daughter; she was worried about paying the rent and the bills. "I felt utterly alone," she says. "We were rejected when we were most in need."

Her abandonment taught her how little the government invests in care. But it was also her first introduction to intersectionality - the idea that different forms of discrimination are overlapping. "I began to see my daughter was going to be doubly rejected as both female and disabled and it absolutely forged me as an activist," she says.

Her awareness of intersectionality has shaped her behaviour ever since. The night before I speak to her, Joaquin Phoenix has expressed his unease at being on an all-white male shortlist in his BAFTA acceptance speech. "I suppose I had a wry smile watching these white men standing up and saying how terrible it was that there was no diversity," she says.

She has walked the walk. Last year she resigned as leader of the WEP to make way for others. "I felt the pace of change wasn't fast enough or systematic enough," she says. "I felt I had been pressed into this very traditional heroic mould of being the person at the top whose voice was the loudest and who goes into battle, and that is not leadership for me. It doesn't leave room for nuance or admitting you don't know all the answers." The party is now led by Mandu Reid, who is black and bisexual .

Today, Walker is chief executive of the Young Women's Trust, which helps low income young women move into better paid work, and co-founder of Activate which funds female community activists to stand for office.

There is, in Walker's perception of the world, a twining of optimism and frustration. On the upside, we have some great feminist role models. She is particularly enamoured of Greta Thunberg who is a hero to Grace, now 18. "It is absolutely electric to see this young woman with autism to take on - as my daughter puts it - these old ableist straight white guys. Greta makes her feel her voice can be heard.”

She is buoyed by the MeToo movement, which has inspired sisterly solidarity. And yet it has also brought out the worst in those men who feel their entitlement is being challenged and who are increasingly being given a platform for their misogyny.

"I think some men have no idea how angry we are," she says. "They have no idea of the scale of male violence against women which keeps so many women in check. Other men know exactly how angry we are. That's why women's anger is so often depicted as hysteria or an excess of emotions: so it can be dismissed. "

Nevertheless, we must persist. That's the message of the book. We must defeat despair and "wield hope as power."

As we wind down, I ask Walker to tell me something hopeful. She says research by the Young Women's Trust found 70% of young women call themselves feminists and one in 10 took part in some form of protest last year.

"This is the great hope for the future,” she says. “This is what keeps me going when things get tough."

Five Rules for Rebellion, by Sophie Walker, is out now on Icon Books, priced £12.99.