The government is coming under pressure to intervene amid concerns that its Covid testing regime for travellers is close to collapse, with thousands failing to be properly tested on their return.

As photos posted online showed drop-off boxes run by Randox, the UK’s largest PCR testing provider, overflowing with unprocessed swabs, growing numbers of returning holidaymakers are reporting that their test kits are failing to arrive, or are taking up to six days to process.

Even before France came off the amber-plus list on Sunday, private testing companies approved by the government were struggling to cope with the demand. MPs and users have led a chorus of disapproval against the testing regime, which looks set to be overwhelmed as more travellers start returning from August getaways.

The Labour MP Ben Bradshaw said he had been inundated with messages from people all over the UK whose test kits hadn’t arrived on time.

He questioned the need for PCR tests on those who were fully vaccinated and returning from countries where Covid rates are lower than the UK.

“They are completely unnecessary,” he said. “It is a complete scam and completely unacceptable.”

There has also been growing anger about the government receiving millions of pounds from the regime – the tests are subject to VAT at 20%.

Martyn Sumners, executive director of AITO, the specialist travel association, said the government should be monitoring whether companies were fulfilling their purpose for the general public.

“People are abiding by the rules with no follow-up. They are paying a lot of money for these tests and not getting results,” he said.

All travellers returning from green- and amber-list countries must take a test before they depart for the UK, and a further PCR test on their second day after arriving home. With PCR tests costing upwards of GBP50 each, households are paying as much as GBP200 for day-two kits.

Those who have not been fully vaccinated must also self-isolate and take a test on day eight if they visited an amber-list country. The tests have to be booked with private firms listed on the gov.uk website.

However, it is increasingly clear that passengers are not being tested as directed. Rory Boland, travel editor at consumer body Which?, said he had seen problems with several testing firms and an increase in every type of complaint. Complaints included tests not arriving on time, people being unable to book tests and misleading prices.

“The system isn’t set up for large numbers, and now many people are travelling the system is not working properly,” he said. “The government might now say it is looking into the prices of tests, but it’s very late in the day and these problems were foreseeable.”

The health secretary, Sajid Javid, has asked the Competition and Markets Authority (CMA) to look into the fees being charged, it emerged over the weekend.

Industry insiders said that some providers were clearly taking on more business than they could comfortably handle via their transport and delivery networks.

Ariane Crampton from Salisbury, arrived back from France with her husband last month.

“We purchased day-five ‘test to release’ PCR tests from Boots at GBP85 each and were told we would receive the results within 24-48 hours,” she said. “My result arrived 55 hours later but my husband’s results took six full working days. Taken together with problems with our other, day-eight tests, the whole exercise was completely pointless.”

The Liberal Democrats have called for a government cap on “rip-off” PCR test costs, and are also demanding that it scraps the VAT on them. The party said this week its research found that, of the more than 400 providers who met the minimum standards to provide PCR tests for travel, 102 were charging GBP200 or more, while only 47 were under GBP50. The most expensive test they found was priced at GBP575. “This compares with Greece and Italy – who have capped their test prices to GBP34 and GBP52 respectively – and France, who provide them for free,” said a party spokesperson.

Which? has published research this month that found that the current cost of testing “is likely to be too expensive for most people, especially families”. It said that an unvaccinated traveller on a return trip to Spain currently required four tests totalling an estimated GBP219 a person. For a family of four, that could add up to GBP876.

The Tory MP Henry Smith, chairman of the all-party Future of Aviation Group, said travellers should be allowed to take much cheaper rapid lateral flow tests on return followed by a “gold standard” PCR only if the first test is positive.

Ministers insist arrivals must take the pricier PCR tests as they are considered more accurate and can be sequenced for mutant Covid strains. But NHS test and trace figures showed that just 5% of swabs are being sequenced.

A government spokesperson said: “We are clear that all private providers must meet a set of required standards, and each provider is held to account, with companies that fail to meet high standards being removed from the list of approved suppliers. The health and social care secretary has requested advice from the CMA to stamp out any exploitative behaviour or poor provision in this market. We are also working with the travel industry and private testing providers to further reduce testing costs.”

Some people have reported that no one had checked whether they had done a day-two test. The Guardian asked the Department of Health and Social Care whether the NHS test-and-trace system checked that people had done the test. It indicated it was not true to say that the NHS test-and-trace system relied on passengers self-reporting the results of their test, and that private test providers were legally required to report test results to NHS test and trace.