If the diamond jubilee celebrations were meant to somehow reflect 21st-century Britain, it was only fitting that two unshakable features of modern life would find their way into all the pomp and silliness. First came yet another example of the screaming hostility that rises up whenever the BBC does anything even slightly untoward, then an outbreak of angst about the growing numbers of people who are expected to work for nothing.

A brief recap, then. On the night of Saturday 2 June, a security firm called Close Protection UK bussed around 80 people from Bristol, Bath and Plymouth to London, where they were to work as stewards in and around the jubilee river pageant. Fifty were classed as apprentices and rewarded to the tune of £2.80 an hour. Another 30 were "customers" of the government's work programme, given training placements with Close Protection UK and promised temporary paid work at the Olympics – but for their travails at the jubilee celebrations, they were paid nothing. Having arrived in the capital on Sunday morning, all of them were told to sleep under London Bridge from 3am to 5.30am. After long hours working in the cold and wet, they then made their way to a campsite in Essex, where they bedded down in conditions described by some of them as "swampy".

The Guardian's Shiv Malik broke the story 24 hours later, and in the following days, everything needed for a national shoutfest fell into place. There was the obligatory phone-in on the Jeremy Vine show, items on Today and Newsnight, and a tour of the studios from an angry John Prescott. Downing Street claimed the incident was a "one-off". In all the debate, though, one big fact was overlooked: that the 30 stewards on the work programme were one small part of a national army of unpaid labour, which seems to be growing bigger every month.

Much of this can be traced back to innovations by the last government, which decisively embraced what some people call workfare – though the coalition has expanded such practices to mindboggling proportions. Sometimes this is a matter of people being forced to work for nothing under pain of having their benefits stopped. Slightly higher up the employment hierarchy, it might be a matter of a jobcentre or work programme adviser telling them a spell of unpaid work will brighten up their CV, or lead to a proper job with the same employer. Politicians praise all these things as a means of getting people into work and thereby attacking unemployment; what nobody mentions is that expanding unpaid labour ensures there is even less proper work in the economy.

On Friday, I spoke to one of the 30 unpaid people at the heart of the controversy. This young woman had been made redundant early last year. Eventually, she was referred by her jobcentre adviser to Tomorrow's People, a charity administering the work programme, and persuaded to train for a qualification in security work. As part of her training, she had already worked for nothing, but only once: at a football match, "observing the crowd and making sure there were no issues", with six other people on the same scheme. When she and others were informed about the jubilee weekend, she said, they were at first told they would be paid around £400, "but at the last minute, they said, 'You're not getting anything – it's work experience'."

Sleeping under London bridge, she said, had been impossible: "It was too cold, it was raining, and there were way too many people." She thus started work at 9.30am, having had no sleep for upwards of 20 hours. She put on her work clothes "in public, in the cold". Breakfast – "piddly", she said – had not arrived until 9.15am. The first chance she had to use a toilet, she claimed, was at 2pm. She was supposed to stop work 12 hours after she started, "but me and some other people gave up, cos we were that cold and wet, at six o'clock." She was then told to take the tube to the end of the Central line, whereupon she called her mother and stepfather almost 150 miles away and asked them to come and get her. "I was that distraught. I had five layers on, and I was soaked through. I was having trouble breathing. After standing up for nine hours, I had a back spasm; I could barely walk. I'd just had enough."

"I'm signing on tomorrow," she said, "and I'm asking to be withdrawn from Tomorrow's People. I can't trust them. I don't want to be treated like dirt, working long hours for nothing.

"There's work experience, and there's slave labour. I wouldn't mind work experience for free if it was in good conditions and I was treated properly … not being asked to change in public and having no access to a toilet." (By way of a response, Tomorrow's People supplied the Guardian with a list of contact numbers for other work programme participants who had been taken to London on an unpaid basis; they proved to be either unavailable, or unwilling to talk).

The companies that either are, or have been, involved in welfare-to-work schemes extend into the distance. As well as charities and social enterprises such as Tomorrow's People, there are the specialist companies that deliver such projects as the work programme (G4S, Serco, the now-notorious A4e), some of which benefit from work experience by giving unemployed people placements in their own offices. Further along the chain are the high-street businesses that take on unemployed people as temporary unpaid workers.

Government schemes that stipulate unpaid work has to be of "community benefit" also involve an array of organisations specialising in supposed voluntary work, which often use unemployed people to staff their offices and shops; there is a lot of noise on activists' websites about the British Heart Foundation, which has 700 such outlets. Its policy director Betty McBride told me that: "As things stand, in every one of our shops, we have work programme placements – some mandatory, some voluntary." The public sector is also involved: last month it emerged that Sandwell and West Birmingham hospitals trust was planning to use unpaid unemployed people on hospital wards, performing such tasks as "general tidying" and "assisting with feeding patients".

What all this means for wider society and the economy is highlighted by the 20 minutes I spent talking to a 22-year-old work programme "customer" from East Anglia (as with just about everyone I've ever contacted about welfare to work, he insisted his identity was kept secret). His last job before nine months of unemployment was with a mobile phone repair company; late last year, he was put on the work programme with the welfare-to-work company Seetec. Seetec recommended that while he continued to claim jobseekers' allowance of £56.25 a week, he should do a four-week work experience placement at a city-centre branch of Argos, which began last month.

"I said I'd only do work experience if there were vacancies at the end," he said. "But at every point Seetec were like, 'They employ people all the time.' And as soon as I went into Argos, the people there said: 'There are no jobs at the end of this.'" He said he tried to leave the placement, but was told that if he did, his benefit would be stopped.

In his first week, he worked for 30 hours ("10 hours more than anyone who was getting paid to work there"), before contacting Seetec and discovering he was only meant to put in 16. "I was doing the bit where you get the item from the warehouse and put it on the shelf, for [the customer] to collect it," he said. When he arrived, he was one of four people on jobseekers' allowance doing supposed work experience; three weeks later, there were six such people, working a variety of shifts, out of a workforce of between 15 and 20.

One man sent to Argos by Jobcentre Plus, he said, had been working unpaid for 30 hours a week in a six-week placement. "No one who was paid was getting overtime any more," he said. "Everyone was being cut down to four-hour shifts. A guy who worked there told me that. The staff were very demoralised that we were taking up so much potential shift work."

Training, he said, was flimsy. Health and safety instruction – "How to walk up a ladder and lift up boxes" – lasted for half an hour, an explanation of the basics of the job and a formal induction took 90 minutes, and that was that. He finished the placement last Saturday, and is now being put on a retail training course: "I said to my adviser, 'I don't know what that entails, but I might as well do it, because it's proper training, not work experience.'"

In response to his story, Seetec said it could not comment on individual cases, but was "investigating the allegation". An Argos spokesperson said the company "understands there are concerns about our involvement in the government work experience programme", but its stores "have clear principles for helping young people into the world of work". She claimed that its policy on placements is to "only use Jobcentre Plus as a partner" and offered to "investigate where another supplier has been used". The six-week placements organised with jobcentres, she said, are offered "only where there is the prospect of a permanent job" and there is always "a training plan that helps the individual go on to secure a job, either within the business or elsewhere". Argos, she said, is committed to ensuring that unpaid unemployed people "work alongside, not replace, paid colleagues".

One particular pressure group has made the running on the issue of unpaid work: Boycott Workfare, one of those nimble, non-hierarchical, online-focused organisations that regularly crash-land in the news. When I spoke to a member of the group called Joanna Long, she said that at any given time hundreds of thousands of people could be working for nothing, undercutting paid workers' terms and conditions, and providing a vast subsidy for the private sector. She also said the group was looking forward to 26 and 27 June, when two judicial review cases against the Department of Work and Pensions will come to the High Court in London. One is being brought by Cait Reilly, the geology graduate who was forced to give up volunteering in a museum and work unpaid in a Birmingham branch of Poundland.

"We're talking about tens of millions of pounds being handed to companies in unpaid work," she said, before suggesting that the issue undermines the fashionable idea that most Britons want to throw people on welfare to the lions. "People know it's their jobs and overtime that are being attacked. So it's not good for them, and they know it's not good for unemployed people either."

Like some of the companies involved, the government is sensitive about all this. Back in February there was a spectacular burst of protest focused on the government's key work experience programme for young people, whereby the unemployed under 25 are encouraged to put in up to eight weeks of work experience – and, as things stood then, risked losing benefit if they left any placement once the first week was up. Zeroing in on this element of the scheme, protesters targeted an array of big retail chains – Tesco, chiefly – and after many companies vowed to pull out, the government pledged to make participation voluntary, while also decrying those who took issue with such schemes as "job snobs". Pressure groups such as Boycott Workfare claim people are still effectively being forced into taking part – and in any case, whether it's voluntary or compulsory, the practice of employing people for nothing is expanding at speed.

Last month, the government vowed to double the numbers of unemployed people forced to work for their benefit – for four weeks at a time, up to 30 hours a week – under what officialspeak calls mandatory work activity, which could mean an increase to around 80,000 placements a year. The coalition is also aiming to create 250,000 work experience places for young people before 2015. The official blurb says the latter are a matter of "voluntary work experience", though when George Osborne announced the scheme last year, he said: "Young people who do not engage with this offer will be considered for mandatory work activity, and those who drop out without good reason will lose their benefits."

Then there is the work programme, launched in June 2011, focused on people unemployed for a year or more, and built around the private companies and charities that are paid according to how many people they get into work. At the last count, around 565,000 people had been referred to the scheme over the six months to January 2012. Unpaid work experience is an inbuilt element of what the work programme offers to its participants. How long placements can last is by no means clear: the government says its so-called "black box" approach means that it is down to the discretion of A4e, Serco et al, and Freedom of Information requests have revealed that at least one work programme provider, the multinational firm Ingeus (owned by the city giant Deloitte), can put "customers" in unpaid work for up to six months.

And so the array of schemes and projects goes on. Some 300,000 people, either suffering from a long-term illness or disabled, are included in what the government calls the work-related activity group, and there have been proposals to introduce many of them to the wonders of mandatory work experience. There is also a pilot scheme called the community action programme (up to 30 hours of unpaid work a week, for as long as six months), and sector-based work academies (combinations of training and unpaid work lasting up to six weeks). All of this points up one of the most sobering things about modern Britain: there may be a paucity of proper work, but there seems to be no shortage of the unpaid variety.

When it comes to young graduates, meanwhile, rules long since imported from the US mean that unpaid work experience is an increasingly obligatory step on the road to professional employment. The thinktank IPPR reckons that at any given time around half of the 250,000 internships in the UK are paid below the minimum wage and 18% – around 45,000 – are wholly unpaid. Note also the government's plans to double the number of people doing full-time paid work in prison, much of it for private companies. Most working inmates are paid very low wages: news emerged this week of the contract for prison work handed to the food packaging company Calpac, which pays an "office manager" £40 for a 40-hour week, and puts a "manual packing operative" on 55p an hour.

To finish, back to our hardworking and comfortably off monarch. Just as the jubilee celebrations got going, the Queen paid tribute to "the continuity of our national story and the virtues of resilience, ingenuity and tolerance that created it". She had a point – but there is also a very British tradition of grim exploitation, embodied by such inventions as the workhouse and the sweatshop. And at this rate, it may be about to return, in spades.