Authorities failed to tell an airline that eight passengers had the coronavirus meaning 200 Brits were not alerted to the risk.
The infected passengers are a group of Hampshire teenagers who flew back to the UK on a Wizz Air flight to London Luton airport on 25 August.
They were diagnosed after getting back home.
Wizz Air said it had not been informed of positive test results and had only become aware of the situation when The Guardian contacted it.
The airline then informed the relevant health authorities in England which are responsible for contacting the 204 other passengers who were on board the flight.
Were you on board the flight? Have you been contacted by the authorities? Email email@example.com
The delay between the flight and the start of the test and trace procedure means countless other people may have subsequently been infected.
Ben Pearce was one of a group of 15 friends who tested positive, eight of whom were on board the Wizz Air flight from Heraklion.
He told The Guardian that he had been called by test and trace handlers multiple times since Friday, but none of them asked for his flight details.
Mr Pearce said each new caller denied having his details on file, despite him declaring them each time.
He also told the publication that he and his group of friends had filled in their passenger locater forms, but they had not been checked at London-Luton airport.
“The phone calls never seem to serve any purpose other than they [the call handler] have been told they need to call you,” he said.
Damian Stafford's 18-year-old son was among the teenagers who tested positive, but he said he had not been contacted by the NHS test-and-trace system.
“It just seemed like a shocking lack of response really,” he told The Guardian.
He said the teenagers had got tested on their own initiative and had not been advised to do so by the government.
The test and trace scheme aims to contact 80% of infected people and their close contacts within 48 hours.
It has missed this target for nine weeks running.
Outsourcing firms Serco and Sitel, who have been tasked with reaching 'non-complex cases', only reached 62% of these people in the latest week.
A spokesperson for Wizz Air said it was not made aware that the passengers had tested positive, but had contacted the relevant authorities since finding out.
They added: "Wizz Air operates all flights in compliance with local travel regulations, and the safety of passengers and staff is the No 1 priority.”
The aviation industry has been pushing for tests to be introduced at airports so those who test negative do not have to quarantine for two weeks when returning from certain countries.
Wales has said it will adopt the proposals but England has not.