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.