National Air Traffic Services (NATS) restored its systems, with capacity returning to normal, late on Wednesday after switching to a back-up system following what it described as a radar-related failure.
The second outage in recent years at NATS, which provides air traffic control services for planes in UK airspace and the eastern part of the North Atlantic, affected Heathrow and Gatwick airports in London, Edinburgh Airport, and other locations.
On Thursday, NATS repeated its apology to those affected, and added that there was no evidence that the incident was cyber-related.
"I know that any disruption is frustrating for passengers. Flights are now resumed ... I will continue to receive regular updates," Alexander wrote on social media platform X, following a meeting with NATS chief executive Martin Rolfe over the incident.
Earlier on Thursday, Alexander said NATS was working closely with airlines and airports to clear the backlog.
A total of 122 flights were cancelled as of early Wednesday evening, with a further 23 cancelled on Thursday morning, according to aviation analytics firm Cirium.
At least 16 flights, including departures to Brussels and Toronto and arrivals from New York and Berlin, had been cancelled at Heathrow Airport, according to its website.
The airport, Britain's largest and Europe's busiest, was hit by a fire at a power substation in March which stranded thousands of passengers.
Ryanair chief operating officer Neal McMahon called on NATS' Rolfe to resign, saying no lessons had been learnt since the August 2023 disruption caused by a  malfunctioning in the automatic processing of flight plans.
