The story of the University of London's cleaners ought to be a modern Made in Dagenham. Immigrant women were scraping a living on a poverty wage from an employer who wanted them to clean up other people's mess and get out of sight when they'd finished. They fought back and, in a rare uplifting moment in these dismal times, won. They forced the university to raise their pay from £6.15 to £8.80 an hour and give them decent holidays and sickness leave.

But no one will make a film about the university cleaners because it lacks the prime ingredient for a feelgood story: a happy ending. Instead, their experience tells a more hypocritical tale about the British attitude to immigrants. Public opinion is set against them. But for all the outrage, Britain still wants foreigners' money, and employers and the middle and upper classes still want foreigners' labour – as long as it is cheap and as long as the workers do as they are told and do not make a fuss.

In 2011, no one noticed the University of London's Latin American cleaners. They travelled on the early-morning buses or trains, when most of London was still in bed, and spent their days doing shifts for two or three different employers. To the academics and students they served they were next to invisible: seen but not noticed; essential but neglected. On the surface, the cleaners, porters, caterers and other contract workers must have looked easy to intimidate. I met Sonia Chura, their leader, and two of her comrades last week. They were all barely five feet tall and couldn't speak English. They were in a strange land that cared nothing for them. "What can they do to us?" their masters must have thought.

As it turned out, they could organise an unofficial strike, get back pay they were owed, attract the attention of the radical press and go on to win better pay and terms and conditions. Their achievement is all the more remarkable because their own union, Unison, did not support them.

Anyone who hopes for a stronger labour movement knows that trade unions must start recruiting the cleaners, shop workers, security guards, carers, maids, nannies and cooks who make up the new working class. By necessity, they must appeal to women and tackle the admittedly formidable task of organising new immigrants. Yet Unison turned on the cleaners.

It found technicalities that allowed it to declare an election in which immigrants ran for union positions invalid. When cleaners protested outside Unison headquarters, its officials locked the doors and called the police. If you want to understand why the British trade union movement is dying faster than grass in a heat wave, the vignette of Unison demanding that the cops control its members tells you all you need to know.

The cleaners did not give up. They joined and helped develop a tiny new union – the Independent Workers of Great Britain. It is organised by Jason Moyer-Lee, another figure who might have stepped out of an inspirational film. He was an American graduate student in London who was appalled by the way employers treated foreign workers and devoted his time to helping them, first in Unison and then in the new union

Now he must help save their jobs. The halls of residence the women cleaned will be closed. The contractors refused to say if they would move the activists to new work. Nor would the University of London, the umbrella body that comprises the London School of Economics, University College London and many another fine liberal institution. I asked its spokesman if the university would guarantee that the women would not be punished for asking for £8.80 an hour. That was a matter for the contractors, he replied. I pointed out that the university paid the contractors. If it said they must keep the activists, the contractors would obey.

"Of course," he said in a sing-song voice, "we absolutely believe in workers' right to peacefully protest." He made the University of London sound like a noble place, while avoiding a promise to ensure that the women were kept on. I later found he had dodged the question for a good reason. As the wretched man was speaking to me, the contractors were telling the activists that not one woman who organised a protest would get a permanent job. I hope they drag them and the university through every employment tribunal they can find.

But even if they lose a tribunal case, the Home Office will not be able to drive them out of Britain. Like so many of the Latin Americans here, they originally moved to Spain. The Spaniards gave them citizenship that allows them to work in any European country. They fled north to avoid the depression the euro crisis brought. As long as Britain stays in the EU, they are safe. They will find other work, too, if they abandon any thought of campaigning for decent treatment. Employers want compliant labour, whether immigrant or native. As immigrants are the easiest to exploit, they will always be popular

It is a nice coincidence that their struggle is taking place in a university. Foreign students are in the opposite position to contract workers. They have money; cleaners do not. Britain wants their cash, but it also wants to get rid of them as quickly as possible. Universities depend on foreigners to subsidise British students – nearly 20% of the output generated by universities comes from non-EU students. Theresa May, however, has driven down the immigration figures by ending the old system that allowed foreign students to pay off debts by working for two years in any job they could find after graduating. The number of foreign students keeping the academic "business" rolling in grew at 5% a year in the last decade but is falling now. I wouldn't be surprised if it fell much further. "We want your money, but we don't want you," isn't the most enticing sales pitch.

The richer parts of London have become creepy places. The streets are deserted and the houses dark. Foreign oligarchs have bought up homes as an investment, thus fuelling the Osborne housing bubble, which provides us with what growth we have, but they don't live in them. What a metaphor for how Cameron's Britain wants its immigrants. If they are poor, it wants them to be invisible, flitting uncomplainingly from one menial job to the next. If they are rich, it wants them to hand over their money and leave. Either way, it doesn't want to see them.