Just three employers have been prosecuted for paying workers below the minimum wage despite HM Revenue and Customs finding 700 who have broken the law in the past two and a half years.

Since February 2014, the government has “named and shamed” 700 employers who have underpaid more than 13,000 workers by over £3.5m. But less than a quarter of a percent of them have been prosecuted under laws that in theory provide for prison sentences in the most extreme cases of wilful non-compliance.

The business minister, Margot James, who has responsibility for the enforcement of low pay laws has conceded that the prosecution rate is “a small number” and is “an issue that causes me concern”.

According to the National Audit Office, the number of workers identified as being owed arrears more than doubled from 2014-15 to 2015-16, rising from 26,000 to 58,000.

James cited the high costs of prosecution and delays that prosecutions cause in securing back pay for affected workers as deterrents to bringing criminal cases.

But Frank Field, the Labour chairman of the House of Commons work and pensions select committee, said the lack of prosecutions showed the government is letting law breaking employers off the hook.

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“The minimum wage is an issue on which the government should want to be proud of its record,” Field said. “But why is it allowing employers to laugh at its attempts to raise the living standards of the poorest and why isn’t it acting more effectively to enforce the minimum?”

The meagre prosecution rate emerged after Midcounties Co-op, the UK’s biggest independent co-op, admitted underpaying a newspaper delivery worker by more than £14,000, the largest payout to a single worker, following inquiries by HM Revenue and Customs about the retailer’s application of the national minimum wage at a store in Maidenhead. It is not yet known if Midcounties Co-op will be prosecuted for this and another case. It has already apologised and repaid the worker and is assessing whether it also underpaid 200 other newspaper delivery workers.

Roger Lilley, one of the workers who received back pay because of underpayment of the minimum wage, on Tuesday wrote to Theresa May, the prime minister and also his constituency MP, requesting her help in raising his case with the business secretary, Greg Clarke and the director general of HMRC, Jon Thompson.

A spokesman for the department for business, energy and industrial strategy which, with HMRC, oversees the application of the minimum wage, said “the government’s priority is ensuring that workers receive the money they are owed as quickly as possible”.

“For this reason, in the vast majority of cases, HMRC seeks compliance using the civil route, which is the quickest way of ensuring workers receive their arrears,” they said. “Under the civil route, employers are not only faced with reputational consequences but also face a financial penalty for breaking the law. Where there is evidence that an offence has been committed the case will always be considered for prosecution.”

The Midcounties Co-op case was the latest of a spate of low pay cases exposed by the Guardian including Sports Direct to the parcel giant Hermes, which delivers for John Lewis and Next.

This week 20 couriers for Hermes, which has been accused of paying rates which amount to less than the £7.20 national living wage, submitted further testimonies to HM Revenue and Customs arguing Hermes is wrong to class them as self-employed. They want to be classed as workers or employees which would guarantee them at least the minimum wage, paid sick leave and holiday and pension rights. The move is likely to increase pressure on the tax authority to launch a full investigation into employment practices at the firm which uses 10,500 couriers.

Their cases were forwarded to Jon Thompson, HMRC chief executive, by Field. He said they showed a pattern which indicated the couriers were wrongly classed as self-employed. They said they are given specific instructions about when they should arrive at work and when to make deliveries during the day; that they do not enjoy the freedom to decide when to take time off as there is a risk their round could be withdrawn; that they are not given a genuine opportunity to negotiate their own fees and that their performance and working methods are directly monitored by Hermes UK.

Hermes declined to comment but has previously said it was confident its service agreements with couriers were legitimate self-employment and confirmed by the HMRC in 2011, but it has said it would cooperate with any new investigation.

It has offered to increase parcel rates to couriers if, after investigation, it emerges they are earning less than £7.50 per hour.