It is a university that prides itself on being a forum for debate about social injustice and inequality. The London School of Economics was founded by Fabian socialists at the end of the 19th century: they believed education was key to liberating society from social ills.

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Last week I was due to attend a debate at the LSE on the expansion of secondary moderns (which is what selection in education really means). At the request of cleaners on strike over their terms and conditions, I withdrew at the last minute. And here is the perverse truth: speakers with good salaries (myself included) will turn up at this prestigious institution to debate the great injustices of modern Britain. Then in come the cleaners – all from migrant or minority backgrounds – to clear up, victims of some of the very injustices that have just been debated.

Like most universities, LSE outsourced its cleaners years ago. It’s cheaper, you see, because the cleaners can then be employed with worse terms and conditions than in-house staff. In this way a university with a multimillion-pound budget can deviously save money on those who clean the libraries, the lecture halls, the offices.

An in-house LSE worker has up to 41 days’ paid leave, six months’ fully paid sick pay, and good maternity pay and pension rights. Cleaners, on the other hand, have the statutory minimum. If they fall ill, they are paid nothing for the first three days, then just £17.87 a day. For a cleaner paid £9.75 an hour – living in one of the world’s most expensive cities – that’s simply not an option. “They can’t afford to be sick,” says Petros Elia, general secretary of the United Voices of the World (UVW) union. Cleaners turn up ill to work instead.

No wonder they describe themselves as “second-class”, “third-class”, or “no-class” workers. The response of LSE’s management is a sobering indictment of industrial relations in a society in which the employers have the whip hand. Cleaners and their supporters have been threatened with arrests and injunctions. “LSE’s mottos is ‘to know the causes of things’,” says Michael Etheridge, the Unison branch secretary, “and yet on the issue of outsourcing it has, as an institution, been wholly ignorant.”

That these cleaners have stood up for themselves – in the face of such hostility – is courageous, and an inspiring precedent for other workers in low-paid, insecure Britain. They’ve come from a variety of different countries; some have only worked at LSE for a few months. But they have organised, and thrown themselves into a determined struggle that now has the university authorities on the run.

Rattled, the LSE has been forced to offer concessions: beginning with 10 days’ full sick pay, then 15, then 20. But UVW and Unison – which represents some of the other cleaners – are clear. This is not a strike simply about improved conditions: it is about being treated the same as other workers. Only parity will do. Unison has been offered a package of improvements, including sick pay of up to 65 days and four weeks of additional maternity pay, and a pledge to work “to reach full parity … in the near future”. But continued pressure on LSE to accept the cleaners’ demands is clearly necessary.

It is a saga that tells many stories about modern Britain. It’s about how, disproportionately, some of the lowest paid and most insecure work is done by migrants and minorities. It’s about a race to the bottom in terms and conditions. It’s about how the law is rigged in favour of bosses. But it’s also about how – with determination and organisation – workers can indeed win.

Mildred Simpson was born in Jamaica and moved to Britain in 1989: she’s worked at the LSE for 16 years. A few years ago she was made a supervisor: back then, there were 25 supervisors, but the number has been slashed to 13. For no extra pay, she is expected to do the jobs of two people. This, for her, is a fight for equality. “We’re doing all the dirty work while they’re drinking their champagne and drinking their coffee,” she says. But she has a message to other workers too. “Fight as well as us as much as you can, for your rights, for pensions, for better working conditions, to be recognised.”

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Britain’s universities grant their management lavish salaries: the Former LSE director Craig Calhoun was on a salary package of £381,000 a year and spent tens of thousands on overseas trips. It’s not just cleaners who are mistreated. Academia is becoming increasingly casualised and insecure. At Birmingham University, for instance, a shocking 70% of staff are on insecure contracts. Academics are overworked, struggling with bureaucracy, and often lacking the basic security of knowing how many hours they’re working each week.

Unions have been dramatically weakened in Britain. That has fed into a general sense that injustice is permanent, a fact of life like a weather system, rather than the consequence of human decisions. If there is no apparent collective means available to overcome injustice, then inevitably we become resigned. But if some marginalised, hitherto voiceless cleaners can put one of the world’s most prestigious universities on the backfoot, they set an example to others. This is a country that has endured the longest squeeze in wages for generations, while wealth at the top and in the boardroom has boomed; where our workforce is increasingly stripped of security and fundamental rights. That might be the current direction of travel, but it can be changed. And those cleaners at LSE show how.