A record number of workers in the UK are being paid less than the minimum wage, a report has found.

An estimated 439,000 people were illegally paid below the hourly minimum wage in April last year, including 369,000 who are supposed to receive the “national living wage” because they are aged 25 or over. The NLW figure was 30,000 more than the previous year and the highest since it was introduced in 2016.

The report by the Low Pay Commission found a higher proportion of women were underpaid the NLW than men, and the youngest and oldest were more affected than other age groups.

The LPC, an independent body, urged the government to restart naming employers who underpay their staff, and to improve enforcement of the law.

“It is vital for businesses to be able to operate on a level playing field and not be illegally undercut on wages,” the LPC chair, Bryan Sanderson, said.

“The government has made real progress with its enforcement of the minimum wage, but more needs to be done to ensure employers comply in the first place and workers know how to enforce their rights.”

When the NLW was introduced in 2016 – vastly increasing the number of people subject to minimum rates – 135,000 people were paid below the introductory rate of £7.20 an hour. It is now £8.21 an hour.

For younger people the minimum hourly wage, which rose slightly in April, is £7.70 for 21- to 24-year-olds, £6.15 for 18- to 20-year-olds, and £4.35 for 16- to 17-year-olds.

Katherine Chapman, the director of the Living Wage Foundation, said that although the report’s findings were shocking, about 6 million people earned less than what she called the real living wage of £9 an hour, or £10.55 in London and were “struggling to keep their heads above water”.

“We need to see more employers commit to pay a real living wage that covers the cost of living, to provide security and stability for workers and their families,” she said.

Rebecca Long-Bailey, the shadow business secretary, claimed the government was not doing enough to crack down on businesses that were breaking the law and exploiting workers. Labour has pledged to introduce a real living wage of at least £10 an hour and increase prosecutions of employers not paying the minimum wage.

The head of the Trades Union Congress, Frances O’Grady, said every worker deserved fair pay for their work. “There can be no exceptions to the minimum wage and there should be no hiding place for bad employers – that’s why the government must restart naming and shaming bad bosses who cheat their workers out of pay.”

Hospitality, retail, and cleaning and maintenance are the industries where the highest number of people are paid below minimum wage. Childcare is the occupation with the highest proportion of underpaid workers.

Companies that had previously been named by the government for paying staff less than the minimum wage included Wagamama, Marriott Hotels, TGI Friday’s, Stoke City football club and Shoe Zone.

The LPC noted that the government did not act on its 2016 recommendation to establish a formal public protocol for the handling of third-party whistleblowing. “Complainants are likely to be discouraged if they do not feel their reports are being responded to,” the report said.

There were several caveats to the LPC’s findings that mean the figures provided are not true estimates of non-compliance. Working out a simple hourly rate for salaried workers is complex, suggesting they may experience higher levels of underpayment than reported; on the other hand, underpayment can be legitimate in some cases, for instance, employers can offset a certain amount of pay if they provide accommodation.

However, the LPC said that even taking into account such caveats, the findings were consistent with a trend of increasing underpayment since the NLW was introduced.

A spokesperson for the government said it was cracking down on employers who failed to pay the minimum wage.

“We have almost doubled HMRC’s budget to £26.3m since 2015, ensuring it has the resources needed to investigate employers who break these rules. HMRC has collected £15.6m of underpayment for over 200,000 workers and issued £14.1m in financial penalties to employers that breached the rules – the highest amount ever.”