An email arrives from a young, discouraged restaurant cook who has recently parted company with her employers. It had been her dream job; the kind of serious kitchen in rural England to which she had long aspired. There was a contract, giving her 40 hours a week on minimum wage. No, she wouldn’t get rich, but she would be doing something she loved.She would be learning on the job. Then the rota turned up: 60 hours a week. With no extra pay. For her labours she would be getting below the minimum wage. She took it up with her bosses. Ach, they said. Standard industry practice. She pointed out it was illegal. Now she is looking for another job.

While she showed me various documents to back up her claims, it speaks volumes that she wouldn’t go on the record. She wants to continue working in the industry and fears being blackballed. She may be very wise. Figures released last month showed that of 700 firms named and shamed by HMRC for paying below the minimum wage since 2014, only three have been prosecuted.

Instead, I went onto social media and invited other cooks to email me with corroborating evidence. As one tweeter put it: “You’re gonna need a bigger inbox.” It was a deluge. Of course, it’s not everybody. In recent months, the likes of Michel Roux Jnr and Sat Bains have cut the numbers of services they’re open for, specifically to attract and retain the highest calibre of staff by offering better terms and conditions. The higher reaches of the London restaurant business report chef shortages, with suitable applicants able to set their own terms.

However, the stories from further down the industry – of young commis chefs simply expected to put up and shut up, of abuse by head chefs, of illegal working practices – give the lie to the glossy media image of life in the kitchen brigade. In these mythical kitchens in magazines and on TV you graft hard and pursue your passion – it’s always about “passion” – encouraged by sympathetic colleagues, and a fair wage.

Part of the problem is young cooks themselves who, as one chef put it to me, “love what they do, love doing it with the freaks and sociopaths around them and don’t care particularly for the world outside their steamy, hot and noisy caves”. They take what they’re given. But a bigger issue is the customer. Every week someone complains below my review online about price. It doesn’t matter whether it’s £50 for two or £140. It’s always too much. They think someone is screwing them.

Yes, there are people getting rich from restaurants. They’re usually the venture capitalists behind the dreary high-street chains, which use economies of scale to keep costs low. As to the rest, it’s a struggle. The middle classes will rally to the cause of low-paid workers in a sports merchandise warehouse but when it comes to the exploited ranks cooking their dinner they moan endlessly about price.

Earlier this year, revered New York chef David Chang wrote a piece for American GQ in which he said bluntly that the business was all but impossible. “The longer chefs look at restaurant math,” he wrote, “the less it adds up for them.”

He described the costs he faced and concluded, “Food needs to get more expensive ...” Ignore him if you wish. Dismiss the young woman who wrote to me as a spineless whinger. But if you do, unscrupulous restaurateurs will simply carry on breaking the law. And all to keep us fed.