On the evening of the day Sayeeda Warsi resigned from the cabinet, in protest at the government’s policy on Gaza, her father called her and told her she could come back to work with him. There was a sense that her high-profile stint in public life was over and she could get back to normal – or as normal as one can be with a life peerage. “I’ve spoken to colleagues who almost grieve about leaving ministerial office,” she says. “Having power taken away from you must feel very different to giving it back. I think I was very lucky. I had a huge world to go back to. Politics was not my social life. I didn’t make it a way of life.”

But we meet in a Whitehall meeting room, not her father’s bed manufacturing business in Dewsbury, and Lady Warsi has not left politics. She was one of the most famous, controversial and outspoken ministers of recent times; her resignation in 2014 was explosive, and she was never going to disappear quietly. She is small and bristles with energy, talking rapidly in a thick Yorkshire accent, and quick to laugh.

Next week, she launches the Baroness Warsi Foundation, which aims, among other things, to improve social mobility. It will give people, and especially young women, opportunities, networks and internships; the stuff that is there for the taking for the kind of people who went to the right schools – or the right school, if you go by the psychodrama being played out by old Etonians David Cameron and Boris Johnson at the top of the Tory party right now.

She refers to the recent Sutton Trust report that found public life and the top professions were dominated by those who had been to independent schools – 74% of judges, for example, and more than half of the cabinet. “It shouldn’t be that 7% [of the population who attend private schools] are in the top jobs where all the big decisions are made. I still think it is tough being a woman, it is tough being from a black or minority ethnic background, it is tough being a Muslim, but it’s really tough being from a working-class background, and that spans gender, race, religion, everything.”

Lady Warsi and David Cameron in 2011. Photograph: Stefan Rousseau/PA

What was it like being in a famously Etonian cabinet (a “preposterous” number, as Michael Gove famously said)? “I think a lot of my confidence and general thick skin comes from being born and raised in Yorkshire,” she says with a laugh. Though she concedes that she did feel “a gentle smugness” when she looked around. “When you grow up in the environment I grew up in, you do grow up with a bit of a chip on your shoulder, and there is something lovely about sitting next to somebody who went to Eton, whose father went to Eton and whose grandfather went to Eton, and you went to the local comprehensive, your father didn’t go to school, and your grandfather had a cart and horse in the Punjab. Who’s done better? Me or him?”

Still, you might argue, social mobility might be less stuck had her government not routinely attacked the poorest families, removed education grants for young people from low-income families, raised tuition fees … social mobility is a much wider problem than can be solved by helping a handful of people through a foundation, isn’t it? “Of course it is, but what we can do is do our bit. I’ve never been one of these people who think because you can’t do everything, you can’t do anything. Me and the other trustees have the opportunity to be able to bring our skillset, experience and networks.”

Between 2010 and 2012, Warsi was co-chair of the Conservative party, succeeded by Grant Shapps, who resigned last November over the bullying scandal that apparently led to the suicide of the young Tory activist Elliott Johnson. In November, Warsi publicly contradicted Conservative claims that they had not been told about the behaviour of Mark Clarke, a party aide who had been named by Johnson as a bully in a letter written just before his death. She had written to Shapps in January last year, complaining about a post Clarke had made about her on Twitter. She added that Clarke was “a disaster waiting to happen, and this was common knowledge”.

Warsi won’t say anything about it today. She has given evidence to the ongoing internal investigation, “and I believe it would be inappropriate for me to start dissecting it now”. Some activists have said they won’t give evidence to the inquiry, fearing reprisals. “I hope people who feel scared about coming forward are given the support and anonymity they need to be able to give evidence,” says Warsi. “It’s in everybody’s interest to make sure everything is put on the table to make sure this doesn’t happen again.”

What she does say is that during her time as chair, “the atmosphere at CCHQ was positive, we had a great team”. Shapps succeeded her as co-chair in 2012. “After that I think things did change. A lot of people who worked with me when I was chairman were subsequently dismissed, and I hope the investigation will look at that, what changed and why it changed.”

She won’t be drawn on whether there is a culture of bullying within the Conservative party, nor whether, for instance, the public spats between Cameron and Johnson set the tone. “Politics is a pretty ruthless place,” she says. “It’s a pretty godforsaken place. If you didn’t fundamentally believe in what you were doing, why would you join this world?” Did she ever feel bullied? “I’d been a criminal defence lawyer – I’d spent most of my 20s and early 30s in police stations. I wasn’t going to be fazed by a few boys who went to nice schools. In that sense, I don’t think I ever felt bullied.” Even though she laughs, it sounds brittle.

She felt frustrated plenty of times, she says. She still does. “For example, recently, on the working family tax credit changes, I couldn’t vote for the government legislation. The question I asked my colleagues at the time was: ‘Has anyone ever been on family credit?’” Her family had received it, or its precursor, in the 1980s. “It was a top-up to support families on low incomes. I know how much that meant to my family, and what a difference it made to the outcomes in our lives. That buffer. I think that worried me more – do some of my colleagues genuinely understand the world we’re in, and the poverty and deprivation that some people live in?”

Warsi is one of five sisters. Her father came to the UK from Pakistan, and worked as a bus driver then a mill worker. He started a furniture business, which became very successful when Warsi was a teenager. At university, where she studied law, she became involved in student politics, but on the left. “Lots of my friends are lefties,” she says with a laugh. But the more she thought about it, the more she realised she was “instinctively a centre-right politician”.

She became a solicitor, working first for the CPS, then setting up her own practice. Her political rise was swift. Oliver Letwin spotted her potential at the 2003 Conservative conference when she made a speech at a fringe event, and she was encouraged to stand in the 2005 election for her home seat of Dewsbury. She failed to win, but the party still planned big things for her. She became Tory vice-chair and an adviser to Michael Howard. Cameron made her a peer in 2007, becoming, at 36, the House of Lords’ youngest member, so that she could serve in the newly created post of shadow minister for community cohesion and social action.

When the Conservatives won the election, Warsi became minister without portfolio – the first Muslim female cabinet minister – and later foreign office minister. She was accused numerous times of just being someone Cameron picked to make his cabinet look less white, male and posh, which of course annoys her. “Ultimately you’ve got to do the job. You can tick every box, but if you can’t do the job, you’ll get found out.” Few politicians have had to endure the amount of personal attacks and sniping – from colleagues, the rightwing press and blogs – that Warsi has over the years. While some of it was grossly unfair, the one criticism she could never properly defend was that she was unelected.

Lady Warsi in the House of Lords for the state opening of parliament in 2012. Photograph: Oli Scarff/Getty Images

Did she ever feel used by Cameron? She pauses. “No, I don’t actually. If I didn’t want to do something, I didn’t, and when I really didn’t want to do it, I left. Had I stayed on and remained now in cabinet, limping on from issue to issue, where I fundamentally felt I couldn’t agree with the government, I’m not sure I would have felt used, but I wouldn’t have had a very high opinion of myself. Because ultimately it’s yourself you have to live with.”

Warsi remains outspoken. In September she called on the government to take more refugees. She won’t say how many Britain should welcome, but says, “more than what we initially announced, and I’m glad we announced greater numbers. Britain has an expertise in certain areas – women subjected to violence and sexual violence in conflict is something we’ve done a lot of work on in recent years, so therefore we should have been the first port of call [for those women] and their families. And unaccompanied minors. We speak about the Kindertransport so often – this was an opportunity for us to repeat that all over again. It would have been a compassionate thing to do.”

She criticised Cameron for a speech he made in June last year about tackling Islamic extremism. “I think he took on board concerns that had been raised by a number of people about the stuff he was saying,” she says now. “The comments about Muslim communities quietly condoning Isis was a particularly low point, but part of it is: does the government have an understanding of these issues? What’s the filter when some spotty teenager at No 10 comes up with an idea? [Somebody should] turn round and say: ‘You know, in the grownups’ world, this isn’t a very clever thing to say or do, and actually it won’t work and is fundamentally wrong.’”

The classic example, she says, was Cameron’s announcement earlier this year that he wanted to help Muslim women learn English, when he suggested not speaking the language could make them “more susceptible” to radicalisation. “Everyone in this country should have the opportunity to learn the language,” says Warsi. “It gives you the opportunity to manage your own life, your own resources, get a job, play a part in society. It’s empowering. Language is the uniting force. How could that announcement have gone wrong? Like I say, some spotty teenager somewhere came up with this great idea to say, ‘The best way to announce it, prime minister, is to make it all about extremism.’” She makes the government sound inept. Is that right? “I’d hate to think such chaos was intentional.” She laughs. “I’d like to give the advisers the benefit of the doubt and say it’s naivety, lack of experience and no real connection to the real world.”

When Warsi warned that Islamophobia had “passed the dinner-table test” in 2011, she was attacked for it. “And actually, tragically, now when I say the same thing, hardly anybody blinks – people know it’s there, people recognise it, the statistics show it, we’ve seen horrific incidents of it. It gives me no pleasure to say I was right, and it does concern me that the government has come to this issue kicking and screaming. The right has to come to terms with why it always seems to find itself in the wrong place on these issues. Whether it’s about race relations, gender equality, sexuality, Islamophobia – we’re always the last ones to come to the table, and we’re usually on the wrong side of history.” (Warsi would include herself in this; she was criticised for homophobic comments and views, and admits she got that “completely wrong … being away from government allows you to rethink some of those positions, and some are ones I’m not particularly proud of”.)

Still, she says she doesn’t look back on her time in government and feel disillusioned. “Government is like childbirth. You forget about all the pain and you just remember all the really good stuff. Being able to chair my party, to represent your government in the foreign office, these were amazing opportunities. I don’t think anything can ever equate the sense of both pride and humility when you feel you are representing your country. I remember those bits.” She enjoyed working with the Liberal Democrats, she says. “There was something wonderful about a coalition cabinet in the end. I think we all tempered each other. I think we made the Lib Dems a little bit more realistic and they made us a little nicer.” She laughs. “It was a good combination.”

Now, she says, there’s time to think and to write (her memoirs should be good; her colleagues are said to have been unhappy that she spent many meetings furiously scribbling notes). She has just become pro vice chancellor at the University of Bolton and is a visiting professor at St Mary’s University in Twickenham. She wants, she says, “some time out reading, lecturing, writing. A clever world, for a while”.

It must be a little galling – now that so many senior Tories are publicly parting with the prime minister over Europe – that she was the one who was attacked for disloyalty. She just laughs. “Maybe I made dissent fashionable. It’s now become mainstream.”