Karren Brady is immaculate – navy dress, navy tights, navy shoes and Chanel belt, her hair perfectly coiffed, exuding warmth and confidence. She directs me to her equally immaculate office at West Ham United, the football club where she is the vice-chairman. Brady sits behind the desk, a Warholesque print of West Ham legend Bobby Moore above her, a laptop in front, and a huge flatscreen TV with rolling news on the wall. Her world seems perfectly composed. You would never guess Brady’s football club is in meltdown and fans are calling for her head.

At 48, and a quarter of a century after becoming Birmingham City’s CEO, she is still known as “the first lady of football”. But, of course, there is much more to Brady than football – numerous business interests (last July, she became chair of Philip Green’s Taveta retail empire); her position as a Tory peer in the House of Lords; an outspoken column for the Sun; aide to Lord Sugar on The Apprentice; mother of two grown children; and champion of women in the workplace. It is in this last capacity that we meet.

Brady has just made a timely TV programme about the gender pay gap. She examines the nature of unconscious bias (how primary schoolchildren distinguish between women’s jobs and men’s jobs, and how employers tend to choose men over women even when they have the same CVs), why women are often paid less for work of equal value, why women can’t ask for more money but men can, and, perhaps most importantly, how working mothers are discriminated against.

Before we start, Brady reaches for her iPhone. “Can I send my daughter a text? She wants me to give her a call. I think she’s had a promotion at work.” She taps away at supersonic speed, then looks up. “Right. So. Have you seen the programme? What did you think of it?”

She reminds me of Max Clifford, another supreme self-brander. Clifford would always start interviews by “receiving” phone calls from, say, Simon Cowell or Beyoncé, thanking him for everything he had done for them. Brady’s narrative is different – this is the woman who has everything: brilliant businesswoman, TV star and supermum. She glances at her huge gold watch. I sense the timer is running.

Brady with David Sullivan, 1993. Photograph: Getty Images

It’s no surprise she has made this programme. After all, on The Apprentice she often pulls up contestants for throwaway sexist remarks, or signals her disapproval with a killer arched eyebrow. What makes her career so fascinating is that, at the same time as championing women’s rights, she has been associated most closely with some of industry’s great unreconstructed dinosaurs – Sugar, Green and the former pornographer David Sullivan, owner of Birmingham City and now West Ham.

The programme is a powerful exploration of gender inequality at work, and makes me wonder how she challenges some of the male attitudes she comes across in the boardroom.

One of her missions in the documentary is to teach women how to ask for a pay rise – she tells viewers she only agreed to appear on The Apprentice so long as nobody was paid more than her. It’s amazing you get paid as much as Sugar, I say, seeing as it’s basically his show. She looks embarrassed. “No, no. I think that came across completely wrong. I did point that out to the makers, actually. Alan is obviously the main person on the show. I meant the roles that are equal to mine – I wouldn’t accept being paid less.”

There’s similar public confusion over her personal wealth, which has been estimated at £85m. “That’s complete rubbish, I’m not worth anything like that,” she says. “That’s Wikipedia. There’s not much I can do about that.” But the beauty of Wikipedia is that you can ask for information to be corrected.

Brady in the House of Lords, 2014. Photograph: PA

In the documentary, Brady is constantly left “open-mouthed” or “speechless” at her discoveries. For example, she says that even though it’s illegal to ask women in an interview if they have children, 46% of employers think this is fine, and 41% think working mothers are a burden on the team. It’s strange she was shocked by this finding. After all, Sugar famously said that if he couldn’t ask women whether they had children, the solution was not to hire them. Has she challenged him on this? She looks surprised. “Well, I have never heard the quote you’ve just put to me, so I’ve never tackled him about it. I don’t know if you’ve ever worked in business, but you don’t go around going raaaah [she roars], having these massive confrontations.” In 2010, I say, you were was asked about his comment in the Guardian. “God, I don’t remember!” she says. “Putting him to one side, my view is that the inference, by asking, is that those women are not as dedicated or hardworking or ambitious. I know myself, from being a working woman, that is not the case.”

Brady grew up in Edmonton, north London. Her Irish father Terry was a self-made, Rolls-Royce driving millionaire, who made his fortune in property and printing. Her Italian mother, Rita, was a full-time mum. She was sent to an all-girls Catholic boarding school, which she hated. “You do what you’re told, you wear what you’re told, you eat what you’re told, you go to bed when you’re told.” It made her ambitious for a different life, she says. “I was sick of being told what to do. The one thing I wanted was independence. And I realised to have that independence, you needed financial independence.” After passing nine O-levels, she left to join the sixth form of a former all-boys school – one of only six girls. She left with four A-levels, but decided she wanted to make money rather than go to university. She joined Saatchi & Saatchi at 18, then went to work for LBC, where she targeted her father’s client, David Sullivan, to advertise with the radio station.

He placed £2m worth of advertising with LBC. Before long, Sullivan headhunted her, bought Birmingham City at her instigation, and, when she was 23, made her CEO. Sullivan bought the club for £700,000 in 1993, and sold it in 2009 for £82m. Much of Brady’s wealth is thought to date back to the sale of the club. By the time she left, 75% of senior management were women.

Brady with Alan Sugar and Nick Hewer on the Young Apprentice, 2010. Photograph: BBC/TALKBACK THAMES/TALKBACK THAMES

Sullivan and Brady remain umbilically tied. In 2010, he bought West Ham United (with former Birmingham co-owner David Gold). Again, Brady was given the job of running the commercial side of the club – though her title was now vice-chairman rather than CEO.The stories of sexism she has faced in football are legion. At her first game as CEO she asked directions to the boardroom and was told “directors’ wives go this way”. When opposition fans chanted “Karren Brady is a whore”, she had to tell her grandmother they were singing “Karren Brady is 24”. Then there is the story of the player who said to her: “I can see your tits in that top.” She is said to have replied: “Well, don’t worry – when I sell you to Crewe, you won’t be able to see them from there.” Is that true? She smiles. “Yeah. Three days later when I sold him, it was the best deal I ever did.” Who was the player? “I can’t tell you. Only because he happens to be a friend of my husband, and he is so embarrassed about what he did that I’ve promised I would never reveal who it was.” She also sold her husband, former footballer Paul Peschisolido, twice, making a profit on him both times. She is at her best telling these stories – funny, lively, a natural performer.

I wonder if she’s ever torn a strip off Sullivan over his views on women. What did she say, for example, when she discovered that he had been a patron of the Presidents Club – the men-only charitable trust that held galas where businessmen were recently caught groping female hostesses who had been asked, in advance, to sign non-disclosure agreements?

She looks aghast. “I don’t think he was a patron,” she says. “Absolutely not. No, absolutely not. He attended many, many years ago, but he didn’t like it and never went again.” Are you sure? “100%.” She asked him? “No, he just mentioned it in passing.”

She answers with such conviction that I assume I have got it wrong. But later I check the Presidents Club brochure that emerged after the event. Sure enough, Sullivan is named as a patron. Although it is true he did not attend this year’s gala, his son Jack – managing director of West Ham Ladies – did.

In the documentary, Brady says the most difficult obstacle facing women at work is returning after maternity leave. After the birth of her first child, she took only three days’ leave. Although many women regard her as a fantastic role model, some would say she succeeded not by championing women’s rights and needs but by hurdling them. Did she feel she had to “man-up” to stand a chance? “It’s not language that I would use. I just felt this overwhelming sense of responsibility that I had to be there, and I couldn’t let people down and I had to bring up a child. And it just manifested itelf in very little maternity leave. It’s something I deeply regret. It’s not something I would ever encourage.”

A few years ago she said she would never take a year’s maternity leave – the amount women are legally entitled to – and that “There would be no CEO, I think, that would take a year off.” Have her views changed since then? “No, because I could not take a year off. I wish I’d taken more time than I did, but not a year.” Does she still believe that no CEO would ever take a year off? She insists she does not remember saying that, and that it is up to the individual.

David Moyes. Photograph: Joe Toth/BPI/REX/Shutterstock

I look at the Bobby Moore painting above her head. It must be a pretty awful time at West Ham – the threat of relegation, the lack of quality transfers, widespread unhappiness with their new ground in what was the 2012 London Olympics stadium (Brady negotiated a bargain rent of £2.5m a year, but fans have complained it was not built for football). There is unhappiness, too, with the manager David Moyes and, perhaps most of all, with the three people at the top of the club – owners Sullivan and Gold, and Brady, whose annual salary is £868,000.

Earlier this month, there was a violent pitch invasion and coins were thrown at the directors’ box. What was even more shaming was that the match marked the 25th anniversary of Moore’s death, and was supposed to celebrate the club icon.

It must have been horrifying, I say. “I don’t want to talk about West Ham,” says Brady, “because this [the TV show] is something that is really important to me, and I don’t want to cloud the two issues. This is something I’ve done on my Sundays and days off to shine a light on the equality issues for women and I would like to focus on that.”

But, I say, the subjects are not unrelated. Some of the attacks target you particularly as a woman. “I disagree. I’ve never heard anybody shout at me. I obviously get social media comments, but I think everybody does in the public eye and you just have to live with that. A lot of the aggression has been channelled at the two chairmen, the two owners.”

She looks at her laptop, and says it is time for her to get on with the rest of her day. Shortly before selling Birmingham City, Sullivan said he had lost the support of the fans and when that happens it is time to walk away. Has that time not come at West Ham? “I’ve never walked away from anything I’ve done, and I’m not going to start now. I genuinely believe the move we made to the stadium is the right one. That’s why we had 52,000 season ticket holders, and why 90% of those renewed.” Again, she says, we are not here to talk about West Ham. I say I have one more question related to women at work.

Last year, after a post-match interview, the then Sunderland manager Moyes told BBC reporter Vicki Sparks that she “might get a slap, even though you’re a woman” because she was being “a wee bit naughty”. Moyes was fined £30,000 by the FA. In her column in the Sun, Brady wrote: “Hopefully the penny has dropped for him that it’s not OK to patronise, intimidate and threaten women and treat them as if they are impostors in a man’s world. End. Of.” Seven months later he was appointed West Ham manager. I can’t begin to understand how she agreed to hiring him.

Did you have no qualms, I begin to say. She cuts me off. “I know what you’re going to say. Can we just concentrate on the programme.” Let me at least ask the question, I say. Again, she cuts me off. “I’ve already made a comment about that, and I don’t want to go there. If you want to talk about the programme, I’m really, really happy to, but I really don’t feel this is an interview about West Ham or talking about my manager or talking about the troubles my chairmen face. I’ve agreed to see you today because it’s a serious issue.” But this issue is about just that – treating women equally at work. “So far you’ve used this programme to attack my chairmen, to attack Lord Sugar, attack David Moyes,” she says.

I’m not attacking them, I say. I’m just asking how you hold men with clout to account when they treat women unfairly. “Whatever ...” she mutters. The smile has gone. Suddenly the room feels very cold. I change the subject. But wherever I head we run into trouble. In the documentary, she bemoans the lack of legislation to ensure women are paid equally for doing jobs of equal worth. I ask what she plans to do about this as a peer. “Well, obviously in the Lords we review legislation so all we can do is keep campaigning for these issues to be pushed higher and higher up the agenda. But I don’t really have any political activities.” How can you say that when you’re a Tory peer? She doesn’t answer.

So we return to the safe territory of Brady’s brilliant career. Yes, she says, she is proud of herself. “When I left school at 18 with no qualifications,” – she seems to have forgotten her nine O-levels and four A-levels – “I didn’t really know what I was going to do with my life. I’ve taken every opportunity, pushed myself in ways I’m not sure I knew were even possible, I’ve made the best of my life and career. So yes, I do feel proud of myself.”

Despite her inconsistencies and selective memory, Brady should be proud of herself. Hers is a remarkable story. She has let nothing hold her back, not even a life-threatening brain aneurysm in 2006. She says this simply made her realise how short life is, and redouble her efforts. She looks at the time again.

What ambitions are still unfulfilled? “I don’t know. The toughest thing about being a success is you’ve got to keep on being a success. You have to do the things you’re passionate about, that you love. Who the hell wants to get to 48 and think: ‘I wish I would have, I should have … I could have done this, I might have done that.’ You don’t really do much in life unless you take risks, push yourself and find your passion.”

At times, it is hard to know what Brady’s passion is. She doesn’t seem mad about football, despite running two clubs for half her life; nor about politics, despite being a Conservative peer. But there is undeniably passion. You can see it in her face, her drive, her hunger to achieve. It’s passion for family, for business, for leading from the front, for being Karren Brady.

I get up to go. She is thinking about the future – what’s left to conquer. “I’m not looking to be a Cabinet minister. I don’t want to be an MP, I don’t want to be mayor of London.” Why not mayor? “Because at the moment I have too much on.” She pauses. There’s a twinkle in her eye, and the warmth has returned. “Maybe that’s an ambition for the future,” she says.

Why Do Men Earn More Than Women? is at 10pm on 4 April, Channel 5