Eight teenage holidaymakers who travelled to the UK from Crete have tested positive for coronavirus.
The boys were on board Wizz Air's flight 8168 from Heraklion to Luton Airport on 25 August.
The airline said 212 people were on the flight but it had "informed the relevant health authorities".
A Department of Health and Social Care spokesperson said it was aware of the situation and was advising those affected to self-isolate.
The teenagers, who are from Winchester, Hampshire, were part of a group of 12 on board the flight and had spent 10 days in Crete.
Shortly after returning to the UK they were contacted by friends they had made on holiday from Estonia, who said they had tested positive upon their return home.
The teenagers later took tests at a local drive-through centre.
'No help from authorities'
Damian Stafford, whose 18-year-old son tested positive, said his family had not been contacted by the NHS test-and-trace system.
"We've simply had to rely on the much vaunted British common sense and do things on our own without any help from the authorities, and what we're doing obviously is self-isolating," he said.
"The track-and-trace system doesn't have to be world beating, it just has to work, and it clearly doesn't at the moment."
The Department of Health and Social Care insisted the system was effective.
It said: "Hundreds of thousands of people are being tested every day and to make sure we stay in control of this virus, we are targeting our testing capacity at the areas that need it most, including those where there is an outbreak as well as prioritising at-risk groups."
In a statement, Wizz Air said: "The airline has now informed the relevant health authorities in England who are responsible for contacting and advising the 204 other passengers who were on board the flight.
"Wizz Air operates all flights in compliance with local travel regulations, and the safety of passengers and staff is the number one priority."
The government has faced growing pressure to decide whether tourists returning to England from Greece should quarantine, after Scotland and Wales introduced their own measures.
Leading figures in the aviation industry have also expressed frustration the government has still not given its backing for testing at airports, akin to systems in place in Germany and France, in order to avoid quarantine measures for those returning from countries with higher rates of infection.
Meanwhile, Greece has insisted it is doing "everything in our power" to keep UK holidaymakers safe.
Last month, a flight from Zante left nearly 200 people facing self-isolation after 16 passengers on Tui flight TOM6215 from the Greek island to Cardiff tested positive for Covid-19.