A Covid-19 testing company co-owned by a former Labour justice minister and a Labour councillor has been accused of failing to deliver kits and test results and not refunding customers, forcing them to fall back on the NHS.

RT Diagnostics is one of hundreds of firms that won government approval to sell PCR tests to travellers planning to enter England, after ministers decided to leave provision to the private sector, under a system that has drawn criticism over allegations of poor service against several companies.

Travellers to the UK have spent at least £500m on PCR tests from private companies since mid-May. But evidence is mounting that the taxpayer-funded NHS testing service, which itself has been outsourced to contractors, is in effect being left to bear the costs when private companies fail.

Customers who paid RT Diagnostics for tests said kits had arrived late or not at all, or that they had never received results. Several said they had been forced to call the NHS, which can offer testing for travellers free of charge in exceptional circumstances.

The company denied the claims, saying in cases of lost kits it absorbed all the costs and refunded individuals 100% of the time.

The former justice minister Shahid Malik and Calderdale councillor Faisal Shoukat are listed as shareholders in RT Diagnostics and Real Time Diagnostics.

Malik has a majority stake in RT Diagnostics, according to Companies House filings, held via a company of which he is the sole shareholder called Premier UK Life Sciences. The company was set up in February 2021, a month before RT Diagnostics was incorporated.

Fred Molin, a university worker based in Hampshire, said he paid £81 for day two and day eight tests in mid-June, before a flight from Sweden to the UK, but has never received them and has yet to be refunded six weeks later.

“They’ve sent me an email saying the refund has been sent but there’s been no money,” he said. “I’ve called them three or four times, whereupon they tell me that their operations are down and they’ll be back up in the next week and a half.”

Molin said he had resorted to calling the NHS, which sent him a test for free.

Khadija Podd said she had found she was unable to register her test on the company’s website and had ended up calling the NHS 119 helpline for advice.

“It wasn’t just the money, I wanted to know if I was committing an offence. But I really couldn’t afford to buy another test. It cost me £168 on top of everything else.”

In an email seen by the Guardian, RT Diagnostics told her it might take “several weeks” for a refund to be processed. After she told them she had spoken to her MP and to the Guardian, Podd received a refund the next day.

“I’m fuming because of the whole system, not just RT Diagnostics, but the whole thing has been so badly done when you compare it to Europe.

“It’s a business here. The UK is using Covid as a business and countries in Europe are not doing the same thing. It has to be called out.”

Rob Crisp, a drum teacher, said the results of tests he bought in June had arrived late and that he had not received a refund, despite requesting one.

He said: “Why should the NHS have to pick up the tab for the failings of a private company who are making a small fortune?”

Paul Myers, the managing director of e-bike company Cooler King, said he still hadn’t received a refund after the company failed to send him test results for a day five “test to release” service purchased in June.

He said the company had promised to refund him in late June but had not done so. “I email them every couple of days and they don’t respond,” he said.

Multiple reviewers on TrustPilot, Google and Twitter said they had received test kits late or not at all – and had not received refunds.

When the Guardian called a customer services number for RT Diagnostics on Wednesday, the person who answered said: “We are out of operations for the moment but we will definitely be back in operations very soon.”

They said customers who had not received tests would “definitely” receive refunds.

They added: “It will be very soon but I can’t commit when it is, but it will be in the next few days.”

A spokesperson for the company denied the claims on Thursday.

“It is a totally preposterous and 100% defamatory accusation that we would not refund anyone whose kit did not arrive,” the spokesperson said.

“For the record, we have a no-quibble 100% refund policy for any kits that get lost via our courier Royal Mail – in these cases we absorb the costs for the lost kit and refund the individual 100%.

“If you are aware of any cases where anyone has not received a refund due to lost kits, please forward us the details immediately.”

RT Diagnostics said Malik was no longer a director of the company and had no managerial responsibility. It also said it was no longer selling test kits and has not been since mid-June. Its website states that tests are out of stock. The company no longer appears on the list of government-approved test providers.

Private PCR testing companies have left a trail of unhappy holidaymakers complaining that test kits, or their results, failed to arrive as promised.

The firms typically charge £80-£200 for pre-bought PCR tests that are mandatory for people arriving in the UK, almost twice the price that passengers pay in Europe.