People with Covid symptoms are being advised to “hack” the testing system by using faraway postcodes to secure tests locally, several have told the Guardian.

Pressure has been growing on the government as people across the UK reported being unable to secure tests locally, with some forced to make round trips of more than four hours and others not getting swabbed at all after only being offered sites more than 400 miles away. Even in England’s 10 worst-hit coronavirus hotspots, many people reported being unable to get a test.

In south-west London, Ellie Bell, a commercial manager, and her husband, a teacher, spent five hours on Monday hitting “refresh” on the government testing website because their two youngest children had coughs.

“Nothing was available except a 135-mile round trip. It was so frustrating, I almost threw the laptop out the window,” Bell said. “The test helpline said it would be quicker to wait out quarantine for two weeks than get a test because they are in such a short supply.”

Bell said her friend recommended she simply go to the London testing centre on Monday. “We got to the test centre and the site staff asked, ‘How many tests do you want?’” she said. “They got us to get a QR code by booking a test in Aberdeen – thus fabricating a postcode to trick the system – and then used those codes to push our tests through. Negative test results arrived the next morning.

“I was completely dismayed seeing the place so empty,” she said. “The staff there were amazing, I think they were relieved to see people. I’ve told another London friend to basically lie her way into a test.”

There were similar reports from Yorkshire. Gavin Kaps, a photographer who had a cough, no sense of smell or taste, a blocked nose and fatigue, was unable to book a test anywhere at the weekend.

“There were literally no options,” he said, so he went direct to a testing centre. “When I got there on Sunday I was approached by a distressed member of staff who I could see had been turning away the cars in front of mine.

“He asked if I had an appointment and informed me that ‘the government’ had said they couldn’t accept people without appointments. He acknowledged the centre wasn’t busy and agreed it wasn’t acceptable that it wasn’t possible to book a test when there was clearly capacity.”

Kaps said a staff member advised him to park in a layby and try to make a booking online. A supervisor then came over and said to use a fake postcode to book an appointment elsewhere.

“He said that if I could do that and get a QR code for the appointment they would let me use that QR code to scan in for a test,” he said. “He went on to tell the rest of the cars waiting in the layby. I tried postcodes in Preston, Manchester, Doncaster, Leeds, Guildford and Sheffield before finding an appointment using a postcode from Glasgow Prestwick, and I booked the appointment.

“I was then allowed straight in as there were no queues. A member of staff approached me and asked for the postcode I had used so that they could pass that on to other people to get a QR code. I obliged. The whole thing was farcical. Someone needs to be held accountable for this. You’ve got to hack the system to get a coronavirus test.”

Afterwards he became concerned the system might believe the centre in Glasgow was experiencing greater demand than in truth. He received a negative result within 24 hours.

The Oxford Mail also said test centre staff had informed people of a loophole to secure a testing appointment.

In the Commons, Munira Wilson, Lib Dem MP for Twickenham, said constituents had secured local tests after being advised to provide an Aberdeen postcode, and she asked whether the health secretary, Matt Hancock, advocated “gaming” the system. “How on Earth is a world-beating test-and-trace system functioning in this way?” she asked.

Hancock said: “It’s incumbent on all of us to take a responsible approach and tell our constituents that tests are available in large numbers and the average distance travelled is 5.8 miles … And people should take this seriously and not game the system.”

Meanwhile, in Bolton, where local lockdown has been imposed owing to rising cases, symptomatic people have also been unable to secure tests locally.

Cath Dodds, a site engineer whose young daughter has a chronic lung condition and asthma, and who developed a cough and a temperature, was forced to make a 240-mile round trip for a test after three days of trying to get one locally.

She said she had to use a fake postcode to book the test, in Carlisle, more than a four-hour round trip away. “This is a hotspot. If it’s so bad in Bolton why can’t we get a test? In the paper we keep reading of new testing centres popping up but we’re not seeing it.”

Of the test centre in Carlisle on Sunday morning, she said: “The car park was empty. We sat there for half an hour and not a single person entered that test centre. I just don’t understand what’s going on.” She is awaiting the results.