The government has asked tax inspectors to consider investigating allegations of low pay by self-employed couriers working for the doorstep delivery company Hermes.

The business minister Margot James has requested that HM Revenue and Customs consider launching a “proactive investigation” into the arrangements used by Hermes, which delivers parcels for John Lewis, Next and other retailers using 10,500 self-employed couriers who are paid per parcel.

Couriers for the company told a Guardian investigation in July that some are earning levels of pay equivalent to below the £7.20 per hour “national living wage”. Others complained of a lack of job security and some said they felt forced to work through illness and bereavement to keep their rounds.

Because Hermes workers are classed as self-employed, the company is not obliged to pay the national living wage, which applies to workers or employees. James said that as part of its role enforcing compliance with the wage requirement, Revenue & Customs could establish whether the couriers were correctly classed as self-employed.

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The ministerial intervention came as 78 current and former Hermes couriers made further complaints about alleged working practices. Frank Field, the Labour MP and chairman of the House of Commons work and pensions select committee, will on Monday send a dossier containing their claims to Theresa May, the prime minister, requesting government action to increase protections for self-employed workers in Britain’s fast-growing “gig economy”.

In his report, some Hermes couriers claim they are not genuinely self-employed because they must work to the company’s orders arriving at the depot by a certain time, must deliver some parcels to time slots and are told they may lose their round if they cannot work the number of days Hermes requires.

One courier told Field’s office they were so afraid of having their work withdrawn if they did not complete their round while they were sick that they worked with a bucket in their car.

Another said: “I broke a bone in my foot, rang up my [field manager] from A&E to explain what had happened, and [they] responded: ‘If you’re unable to work or find cover I’ll withdraw your work.’”

Field said some of the accounts suggested “appalling bullying” from some staff, who “seem to be enforcing an employee contract under the cover of self-employment”.

He said the claims meant there should be “a sea change in the treatment of couriers’ requests for time off to grieve, care for a loved one, recover from their own illness or take a short break”.

In response, Hermes said it was confident its service agreements with couriers were legitimate self-employment and said this was confirmed by the HMRC in 2011, but said it would cooperate with any new investigation. It said it was unable to comment on the allegations in Field’s report without knowing more detail, but said it would fully investigate issues raised by the couriers. It said it does not believe the report reflects the way Hermes operates and said the 78 complaints represented less than 1% of its workforce.

Facebook Twitter Pinterest The business minister Margot James. Photograph: Antonio Olmos/The Observer

It also said that more than a third of couriers have worked with Hermes for at least five years and that it is “committed to ensuring that everyone at Hermes operates in a supportive and compassionate manner. If we find that these standards have not been met we will take the appropriate action.”

Hermes last month had to apologise to a courier in Scotland who lost his rounds because he fell behind with deliveries while he looked after his wife, who was dying of cancer.

The possibility of a HMRC investigation and the latest allegations about working practices come as Hermes begins to take internal action to counter complaints of low pay and poor treatment.

Following the Guardian’s investigation, it has launched a “service provider complaints panel”, which has already received 36 complaints, 16 of which have been upheld. It has also offered to increase piecework rates paid to couriers if, after review, it finds the courier does not have the potential to earn at least £7.50 per hour. Of four couriers who complained about pay in recent weeks, three have so far received increases.

Eleven couriers claimed to Field that they were paid the equivalent of well below the national living wage. One said that working long hours on rural rounds meant their pay worked out at less than £3 an hour, while another said they earned about £6 an hour because they had to drive 12 miles to start their round.

“We have chosen to exceed the national living wage and have set our minimum standard at £7.50 per hour, taking into account any expenses the couriers may accrue,” Hermes said. “We are confident in the accuracy of our courier pay model and our records clearly show that our average courier rate is £9.80, 36% above the minimum wage, after all legitimate expenses have been deducted.”

It also said it was putting in place an independent ombudsman to handle complaints and was this month issuing a new code of conduct to staff, demanding that managers treat couriers with “dignity and respect”.

Field wants a government investigation into the use of self-employed workers at Hermes and other firms. The latest official data shows 83% of new jobs created in the UK between March and May were self-employed positions, which means they do not benefit from sick pay, paid holiday, pensions or employment protections.

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In her first speech as prime minister in June, May directly addressed people who “have a job but you don’t always have job security”, saying: “The government I lead will be driven, not by the interests of the privileged few, but by yours.”

“This is the prime minister’s first serious test of her commitment,” Field said.

In a letter to Field last week, James said she was monitoring the situation at Hermes and signalled her determination to clamp down on any inappropriate use of self-employment in the British economy.

“While I am unable to comment on the particular examples you refer to [at Hermes], I believe everyone deserves to be treated fairly at work, free from intimidation and abuse,” she said.

“Employers cannot opt out of their employment law obligations by defining individuals as self-employed. An individual’s employment status is established based on the reality of the working relationship.”

Field claims Hermes has been enjoying “almost exclusively the benefits of self-employment, namely that it is not obliged to pay employers’ national insurance and pension contributions, and is not covered by employment regulations covering the national living wage, holiday pay and sick pay. Yet the couriers themselves are enjoying few, if any, of the benefits.”

The results of any HMRC inquiry into the self-employed status of the firm’s 10,500 contractors are likely to be closely watched by other firms in the so-called gig economy.

Companies such as Uber and Deliveroo also rely on self-employed workers who do not receive sick pay, paid holiday, pension contributions or employment protection, but enjoy flexibility about when and how they work.