The government has launched a crackdown on unpaid internships, sending more than 550 warning letters to companies and setting up enforcement teams to tackle repeat offenders.

HM Revenue & Customs is expected to target sectors such as media, the performing arts and law and accountancy firms, which have a reputation for using unpaid interns.

It will also issue guidance to employers spelling out when they are legally obliged to pay at least the national minimum wage to interns.

About 70,000 internships are offered each year in the UK, according to the Sutton Trust social mobility charity. It estimates that of 10,000 graduates who are in internships six months after they leave university, a fifth are unpaid. It has calculated the cost of doing an unpaid internship as more than £1,000 a month in London and £827 in Manchester, putting valuable work experience beyond the reach of those from families on low and middle incomes.

Although minimum-wage legislation makes many unpaid internships illegal, the government recently admitted that there had been no prosecutions. Campaigners want the law to be tightened to ensure all internships are paid, fairly advertised and awarded on merit rather than through contacts. They want to make it easier to report unpaid internships to HMRC and to introduce tougher penalties for those found breaking the law.

The business minister, Andrew Griffiths, said: “Employing unpaid interns as workers to avoid paying the national minimum wage is against the law and exploitative. No one should feel like they have to work for free to get the skills and experience they need to get ahead.

“That’s why over the last three months, government enforcement teams have been targeting employers advertising for unpaid interns, reminding them of the law and the consequences of breaking it.”

The government has promised to review the existing policy and legal framework and will consider what other action can be taken if its enforcement crackdown does not force change in the behaviour of companies.

Under employment legislation, anyone who is acting as a “worker,” an official employment classification, must be paid. However, defining a worker relies on multiple factors, which might include an expectation that the person turns up for work each day.

In its response to the Downing Street-commissioned Matthew Taylor review on working practices published this week, the government said: “An employer cannot avoid paying someone the minimum wage simply by calling them an ‘intern’ or saying that they are doing an internship.”

But it said “genuine volunteers” were not entitled to the minimum wage and campaigners say that unscrupulous employers are using this as a loophole to avoid paying.

Campaigners have called on the government to make it easier for employers and their staff to identify how their roles should be classed. There was disappointment that the government only promised to consult on clarifying employment status in its Taylor response.

Sir Peter Lampl, the founder and chair of the Sutton Trust, said: “Unpaid internships remain a serious barrier to social mobility so any move to crack down on employers who continue to take them on should be welcomed. But little is likely to change until legislation around internships is made clearer.

“Many employers either remain unaware that their interns should be paid, or are choosing to exploit the lack of clarity in the law – through work shadowing placements, for example – to avoid paying their interns.

“It’s clear that the current law is not working – at the end of 2017 there were no prosecutions in relation to interns and pay, yet tens of thousands of young people continue to work for free. We want to see tighter legislation so that all internships are paid at least the national minimum wage, fairly advertised and awarded on merit.”

Tanya de Grunwald of Graduate Fog, a campaigner for fair internships, said the HMRC complaints process was too slow and lacked transparency and accountability.

“It is time for HMRC to admit that the reporting system for unpaid internships is not fit for purpose,” she said. “For starters, it relies almost entirely on interns coming forward to complain about their former employers – something few are brave enough to do, for obvious reasons.

“We also need much tougher penalties for employers caught breaking the law. In most cases, employers are simply asked to pay the intern back pay at minimum wage level.”

De Grunwald said she had recently reported top fashion title Vogue to HMRC for offering month-long unpaid “workplace shadowing” posts, which involved sourcing clothing samples for photo shoots, transcribing interviews for journalists and other work important to the day-to-day running of the magazine.

She said: “Unpaid internships take advantage of those who do them, entrench privilege and exclude diverse talent. Vogue’s four-week placements may be short, but unless they pay a wage they are out of reach for most young people, who simply can’t survive in London for a month without any money.”

A spokesperson for Condé Nast, the publisher of Vogue, said that those undertaking workplace shadowing were “in the office to learn, are entirely free to attend external meetings and interviews, and are not obliged to come to the office every day”. The spokesperson said the publisher was therefore under no obligation to pay the national minimum wage but did give some travel expenses.