Aviation chiefs will meet Transport Secretary Mark Harper on Friday as the knock-on effects of the air traffic control (ATC) failure continued.
The boss of easyJet has demanded that a “full independent review” is carried out into Monday’s problems, which have caused widespread disruption.
The airline’s chief executive Johan Lundgren said the incident, which wrecked the travel plans of around a quarter of a million people this week, “must not happen again”.
Flights to and from UK airports were restricted for several hours on Monday afternoon as National Air Traffic Services (Nats) were unable to process flight plans automatically.
Mr Harper said he would meet Nats, the Civil Aviation Authority, Border Force, airlines, airports and trade groups on Friday “to discuss the latest situation ahead of the start of the new school year” in England, Wales and Northern Ireland.
Nats said an “unusual piece of data” it received forced it to switch to manual checks.
More than a quarter of flights were cancelled on Monday, and the knock-on effect continued for two more days.
Thousands of holidaymakers are still stranded overseas as many flights from popular destinations are full.
Mr Lundgren said: “We have been absolutely focused this week on helping our customers impacted by the ATC failure return home.
“An incident of this scale should not have happened and must not happen again in the future.
“Passengers deserve to see a full independent review, which not only results in meaningful improvements to prevent an incident of this scale happening again but also considers a wide range of issues beyond this incident, including staffing levels required at Nats to deliver today’s flying and what modernisation is needed to deliver the flying of tomorrow.”
An independent investigation was carried out into the failure of Nats’ systems in December 2014 which also caused widespread flight chaos.
Nats is conducting its own inquiry into what happened, and will send a preliminary report to Mr Harper on Monday.
Mr Harper said: “I’m closely monitoring the latest developments following Monday’s air traffic control failure.
“Although operations have nearly returned to normal, many people are still waiting for their rebooked flights
“Airlines have worked incredibly hard to fly passengers back, and I remain in contact with industry to ensure we’re doing everything possible to get passengers home as quickly as possible.”
This week’s disruption came at one of the worst times of the year as there is little spare capacity due to it being the end of the summer break for many schools.
Analysis of airline websites by the PA news agency showed most flights to the UK from popular destinations such as Majorca, Crete, Sicily and Antalya are sold out until the weekend.
Flights with spare seats are priced at more than £400 to deter new customers from booking them.
EasyJet said it is trying to fly people back as quickly as possible.
It said in a statement: “As more seats become available we are contacting customers who we know are yet to return home to try and get them on earlier flights.
“Seats on these flights will be offered on a first come, first served basis so we encourage those who wish to travel earlier to call us as soon as possible on +44 (0)330 5515147.”
British Airways said it will continue to reduce the size of its business class cabins on popular short-haul routes to maximise capacity.
This involves selling the middle place in rows of three seats, which are usually kept empty in that part of BA aircraft.
