Air passengers to the UK have spent at least GBP500m on PCR Covid-19 tests from private companies since mid-May, a Guardian analysis has found, only for the NHS to be saddled with extra costs when firms fail to deliver them.

Concern is mounting that the system for testing travellers is on the brink of collapse, with Heathrow airport calling on Wednesday for the government to allow people to use cheaper lateral flow tests instead.

Travellers have reported having to call the NHS testing hotline on 119 for free taxpayer-funded kits after PCR tests they had paid for did not arrive.

Sandra Parrish, a nurse, said she had been told by NHS Test & Trace to call 119 when tests she ordered from Luxembourg-based Eurofins did not arrive on time.

Her day 8 test, ordered from the same company, was also delayed. Sandra said she had asked for a refund from Eurofins after spending GBP80 with them, but has yet to receive one.

“When the test didn’t turn up, [Test & Trace said] dial 119 and it was sent from the NHS. All that resource used and we had already paid all that money.”

In the end, she paid for a day 5 test in order to go back to work sooner, spending GBP180 in total. She said: “I got a Covid bonus for working for the NHS – after tax it was less than that.”

The Guardian has approached Eurofins for comment. An email sent by the company to Parrish blamed “logistical problems” for delayed delivery.

Bottlenecks in the system have built up amid a significant increase in the number of flights being taken since foreign travel for leisure purposes became legal in Britain on 17 May.

Heathrow said its terminals hosted 1.5 million passengers in July, a rise of nearly 58% on June, after restrictions on travel were further loosened for those who have had two vaccine jabs.

If the increase seen at Heathrow is matched at other major airports, which are yet to report figures, approximately 4.2 million passengers would have flown during the month.

Coronavirus rules governing the busiest air travel routes mean most will have had to take at least one PCR test. Test kits cost an average of GBP75 each, indicating that air passengers spent at least GBP315m on them during July.

One aviation analyst said the Guardian’s estimate was credible and provided a parallel figure of GBP186m for the period between mid-May and the end of June, based on flight data and travel restrictions imposed by different countries.

Travellers spent at least GBP500m combined on tests between mid-May and the end of July, the analysis suggests. However, the true figure is likely to be significantly higher, given the fact that many passengers will have had to take multiple PCR tests if they were not fully vaccinated or if they were fully vaccinated but returned home from an amber list country before the quarantine exemption was brought in for this group on 19 July. The passenger increase at airports may have also been higher at airports other than Heathrow, which caters more to long-haul passengers.

“Government must now capitalise on the vaccine dividend and seize the opportunity to replace expensive PCR tests with more affordable lateral flow tests,” said Heathrow’s chief operating officer Emma Gilthorpe.

“This will ensure travel remains attainable for hardworking Brits, desperate for well-earned getaways and keen to reunite with loved ones before the summer travel window closes.”

The consumer group Which? said it had warned the government several times to expect the “entirely foreseeable” chaos engulfing the travel testing system.

Rory Boland, Which? travel editor, said: “These are government mandated tests, so it’s essential the government takes responsibility for ensuring travel is affordable for all UK consumers … The Competition and Markets Authority should move quickly to ensure that action is taken against any rogue operators in the testing market, such as those charging excessive or misleading fees for tests.

“The government must also introduce robust accreditation for all test providers listed on its website, to prevent travellers being ripped off when trying to buy something as essential as a test.”