ITV News Meridian's Andy Dickenson has been speaking to the holidaymakers about their ordeal.
A family from Essex have shared their distressing ordeal of sleeping on an airport floor for two days after their flight home was cancelled because of a technical fault.
National Air Traffic Services says the glitch has been fixed and systems have been running normally since 2.30pm on Monday.
Repatriation flights have started bringing passengers back but disruption is expected to last several more days.
Holidaymaker Chanel Acheampong from Basildon and her party of 13 are among those waiting for flights home and said members of her family became "unwell" due to the stress.
Ms Acheampong said: "We’ve been treated like animals, we’ve been sleeping on the floor like cockroaches.
"I have a nephew who has a heart condition who managed to get on a flight last night after he had four attacks at the airport.
"I have a niece with half an insulin vial which will only last her until tomorrow.
"My son had a migraine because he was stressed out and threw up everywhere."
Ms Acheampong's nephew has been put on a flight back to the UK. Eight members of her party have been offered a flight to Tenerife tomorrow morning and then a ferry back to the UK.
A spokesperson for easyJet said: "We are truly sorry for the experience of Chanel and her family which is clearly incredibly difficult for them.
"We are in contact with her and working on options to get them home as soon as we can.
"Our teams have been working around the clock since Monday to help our customers as quickly as possible.
"As this is one of the busiest weeks of the year this is very challenging however we are providing hotel accommodation where it is available and operating additional repatriation flights as well as larger aircraft on many routes.”
Gatwick Airport has reported its half-year pre-tax profits which have jumped by two-thirds today, to £100 million.
CEO of NATS, Martin Rolfe said: "I'd like to start by apologising for the significant disruption that the failure on Monday of the air traffic control system gave to everyone.
"We don't underestimate what's happened and are working incredibly hard with the airlines to make sure everybody can get home safely.
"We are confident that we are in a position where this particular problem can’t happen again.
"There'll be a full investigation and the Secretary of State will receive that letter on Monday."
NATS said that situations like this are rare and the last time, something like this happened was 10 years ago.
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