Nats said: "We have a technical problem with a system at the Swanwick Air Traffic Control, which is causing some flight restrictions".
Isle of Man air passengers have been unable to get to Gatwick overnight after extreme weather has caused delays.
The Met Office said Thursday was potentially the UK's hottest ever day after it received a provisional recording of 38.7C at Cambridge Botanic Garden.
Gatwick Airport advised passengers to check with their airline for updates.
British Airways said it had been affected by severe weather conditions overnight as well as by the technical issue.
Elsewhere, there was disruption on the Midland Main Line between London St Pancras and Sheffield and on services operated by Great Northern, Thameslink, East Midlands Trains and West Midlands Trains.
"We apologise for any inconvenience people may be experiencing, and will provide further information as soon as possible".
Air traffic control company Nats reported a technical problem at its Swanwick centre in Hampshire, which controls airspace across the southern United Kingdom, shortly after noon.
European air traffic co-ordinating agency Eurocontrol said the problem was caused by an "issue with radar displays".
"Everything was done to keep trains moving where possible, and last night hundreds of staff were out fixing the damage and repairing the railway ready for today".
Having earlier warned against making non-essential journeys, Network Rail later urged passengers to check for the latest service information before they travel.
Heathrow, which saw a record-breaking 37.9 Celsius (100 degrees Fahrenheit) yesterday, said: "Flights are now arriving and departing at Heathrow, and we are supporting NATS to resolve the issue as quickly as possible".
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