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As thousands of passengers waited at Gatwick Airport, south of London, police hunted unsuccessfully for the operators of the large drones, which reappeared near the airfield every time the airport tried to reopen the runway.
Police said there was no indication of a terrorism motive behind the devices, which first appeared on Wednesday night (local time).
"We will be deploying the armed forces," Defence Minister Gavin Williamson told reporters. "We are there to assist and do everything we can."
By 5pm on Wednesday, easyJet, the biggest operator at Gatwick, said it had cancelled all flights on Thursday because it did not know when the runway would reopen.
The airport said flights would remain shut down until further notice on a day when 115,000 people were scheduled to pass through, many en route to seasonal breaks.
Prime Minister Theresa May's spokesman condemned the standoff as "irresponsible and completely unacceptable".
Passenger Ani Kochiashvili had been bound for Georgia but spent six hours overnight sitting on a plane with her children.
"I'm very annoyed because I'm with two kids, a three-month-old and three-year-old," she told Reuters by phone among thousands camped in the terminal.
"They require a lot of space and food and changing and all that, and the airport is crazy busy so it's challenging."
Flights were halted just after 9pm on Wednesday after two drones were spotted near the airfield, triggering the biggest disruption at Gatwick since a volcanic ash cloud in 2010.
Police said more than 20 units were hunting the operators near Gatwick airport, 50km south of London.
Transport minister Chris Grayling said it was clearly a deliberate act. "This is a commercial-sized drone," he said. "Every time Gatwick tries to reopen the runway, the drones reappear."
Grayling temporarily lifted night-flying restrictions at other airports to ease congestion caused by diverted aircraft, Sky News reported.
With an upsurge of public enthusiasm for drones, there has been an increase in near-collisions by unmanned aircraft and commercial jets in recent years.
The number of near misses between private drones and aircraft in Britain more than tripled between 2015 and 2017, with 92 incidents recorded last year, according to the U.K. Airprox Board regulator.
Richard Parker, head of air traffic management technology firm Altitude Angel, said this was the first time a major airport had been hit by such a sustained and deliberate incursion into its airspace.
"It's sophisticated, not from a technology side, but it's organised. People have charged lots of batteries, and are deliberately trying to avoid being caught, probably by driving around to different locations," he told Reuters.
"It really is unprecedented."
Gatwick's Chief Operating Officer Chris Woodroofe described one of the drones as a heavy industrial model.
"The police advice is that it would be dangerous to seek to shoot the drone down because of what may happen to the stray bullets," he told BBC radio.
Drone expert Peter Lee of Portsmouth University said he and others had been anticipating disruption.
"One of my concerns about today is that it may well encourage copy-cat incidents because you can achieve a high amount of disruption for a very, very low cost," he said.
It is illegal to fly drones within 1km of a British airport boundary, punishable by five years in prison.
Even after Gatwick reopens, the backlog and disruption are expected to last for days.
Gatwick said that it was working with its airlines, the biggest of which also include British Airways and Norwegian, on recovery plans once the runway re-opens.
Safety was its "foremost priority," it said.
Gatwick, which competes with Europe's busiest airport Heathrow, west of London, had previously said Sunday would be its busiest day of the festive period.
Passengers took to Twitter to share their stories.
One waiting at the airport said: "At Gatwick Airport, drone chaos, surprisingly good natured, but complete mayhem."