The biggest fight of Consuelo Moreno Yusti’s life began at a bus stop. For the next 11 years, she took on a giant multinational and a venerable university. Last month, she won. She won the kind of fight they tell you just can’t be won. She used tactics the rest of us might learn from. And her victory could change the lives of thousands of other people in Britain.

But I’m getting ahead of myself. Let’s start at that bus stop in 2006. Waiting there are two cleaners from the University of London’s School of Oriental and African Studies (Soas). Moreno Yusti is telling her friend Maria how her hours have been cut from the five a day stated in the contract to just three. How will the family cope on even less money? Maria pulls out a business card and almost whispers: “Go there – but don’t say I was the one who gave you this.”

The card carried the details of a trade union. Back then, unions inspired fear among Moreno Yusti and her colleagues. They worked at one of the most leftwing colleges in Britain, but were employed by an outsourcing firm that had no truck with unions– like so many other companies.

Moreno Yusti, a mother in her late 40s, still cleans at Soas. She wakes at 2.30am, buses in to work before 4am. Then it’s 10 hours a day, five days a week. When term starts this month, things will get really hectic. She deals with overflowing toilets, with people taking a shit in the showers, or leaving turds on toilet lids. Saturdays are easier, because Moreno Yusti only comes in for 6am.What did she get in 2006 in return for her burning eyes and aching back? Her contractual rights had just been ripped up. Some colleagues hadn’t been paid for three months – just before Christmas. So when a union sorted out her hours and the missing back pay, she became an organiser for Unison. Widespread fear meant she had to recruit “on the downlow”. “Everyone would say, ‘I want to keep my job, look after my kids.’” And she’d retort: that’s the point of a union! “It was harder work than cleaning.”

For Soas, a prime attraction of outsourcing was to make cleaners, caterers and security guards someone else’s problem.

The cleaners had one big goal – to be directly employed by the college they worked at, rather than through another company. Top of Soas’s values is “promoting equality and celebrating diversity” – yet members of its own community suffered economic apartheid. Unlike direct employees, the cleaners got no sick pay, hardly any holiday pay and the minimum wage. They cleaned up after lectures on worker exploitation – a subject on which they were the experts. Why shouldn’t the cleaners be made equal? Impossible, everyone said.

Lenin Escudero, another cleaner and a campaign strategist, remembers: “Even friends would say, ‘Lenin, you’re a nice guy but give it up. You can’t beat the system’.” This is what activists always hear. It’s what McDonald’s strikers were told last week: you’re on to a loser; if you hate it so much, quit – presumably so some other poor sod can be exploited.

The cleaners were nearly all migrants and almost none could speak English. Neither could Moreno Yusti, even though she had studied law back in Colombia. However serious the complaints lodged with their outsourcing employer, they’d go ignored. Every day found some new way to tell them that they were the lowest of the low.So Moreno Yusti and Escudero recruited outside support. They got the student union on board, badgered professors in the corridors. In turn, they began to pressure Soas management to take some responsibility for those men and women who kept the students safe and the classrooms tidy. In 2008, the cleaners won sick pay, more holidays, and a London living wage. Their victories drew in more union members and emboldened cleaners at nearby campuses, such as Birkbeck.

In June 2009, Soas cleaners finally forced outsourcing firm ISS to recognise their trade union. Days later, they were summoned to an early-morning meeting on campus, ostensibly to discuss shift patterns. Doors were blocked and when ISS representatives mentioned the phrase “immigration papers”, immigration officials in riot gear stormed into the hall. They checked everyone’s status. Nine members of staff were bundled into lock-ups, then on to planes. Among them was a heavily pregnant woman.

According to Soas documents I’ve seen, ISS managers admitted to calling in the immigration officials months beforehand. The raid galvanised students and teachers. It had happened on Soas property with college managers on hand. Soas told me that none of its managers “had any prior knowledge” of the raid – but a note I’ve seen from its then head of HR states, “Soas was informed of the impending visit” weeks beforehand. When I asked the company why it called in immigration officials, it declined to comment on any questions. Similarly, it declined to discuss any of the other issues raised.

For Soas, a prime attraction of outsourcing was to make cleaners, caterers and security guards someone else’s problem. The raid made that untenable: student protesters were now occupying the director’s offices; walls were covered in graffiti. And ISS kept mismanaging the Soas workforce – by, for instance, finding one of its supervisors guilty of sexually harassing an employee and then bringing him back to work on the same contract – causing more outrage and forcing the college to intervene over and over.

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Moreno Yusti and her colleagues had effectively exhausted their employer. I have covered many such outsourcing contracts before, including at nearby colleges. To make big profits on basic services, the outsourcers hammer workers’ pay and conditions. Force them to treat staff with a modicum of respect, and the business model collapses. So much was confirmed by a college report last year, which found that bringing the cleaners, the caterers and security staff back in-house would be “cost-neutral”. The savings the college had made were purely from exploitation of its lowest-paid staff – and, as the report noted, neither the trade unions nor the student union would stand for that any more.

Last month, Soas bowed to the inevitable and announced it would bring all facilities staff in-house. Moreno Yusti had won the unwinnable. She won’t be the last. Cleaners at the LSE have just won the same battle, and across London migrant workers are gearing up for similar fights for higher pay and greater dignity.

In all the years she has lived in Britain, Moreno Yusti has had stereotypes placed around her neck. The little woman. The ignorant foreigner. The migrant happy to undercut others’ wages. The reality is she fought harder and smarter than a multinational and know-all university managers. And she has levelled up pay and conditions for 120 workers.

At the end of our chat, her daughter Maria stops translating and says simply: “I think she’s amazing.” So do I. And my bet is there are thousands like her, some of them working just under your nose.

• Aditya Chakrabortty is a Guardian columnist