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"We are responding to a drone sighting at Heathrow," the airport said. "As a precautionary measure, we have stopped departures while we investigate. We apologise to passengers for any inconvenience this may cause."
London's Metropolitan Police said they had received reports of a drone near the airport at about 1705 GMT on Tuesday, which they were investigating with airport authorities.
The airport confirmed about an hour later that take-offs had resumed. Flight tracker websites showed flights departing from 6.11pm.
A Reuters witness in a plane on the runway at Heathrow said multiple aircraft were waiting for permission to take off before being later told that things were starting to move .
London's second busiest airport, Gatwick, was severely disrupted when drones were sighted on three consecutive days in December, resulting in about 1,000 flights being cancelled or diverting and affecting 140,000 passengers.
Gatwick's drone nightmare - the most disruptive yet at a major airport - exposed a new vulnerability that will be scrutinised by security forces, airlines and airport operators across the world.
The British army was forced to deploy military technology to guard the area around Gatwick, reassuring the airport that it was safe enough to fly.
British Transport Secretary Chris Grayling said on Tuesday the military was preparing to deploy the same equipment at Heathrow.
"We are in contact with Heathrow Airport concerning the drone sighting," he said.
"I have already spoken to both the Home Secretary and Defence Secretary and the military are preparing to deploy the equipment used at Gatwick at Heathrow quickly should it prove necessary."
Both airports responded to the Gatwick incident by ordering military-grade anti-drone technology.
Heathrow said it was working closely with authorities including the police and looking at relevant technology to combat the threat of drones.
The airport handled 78 million passengers in 2017 and is the main hub for British Airways. Its busiest routes in terms of passengers numbers are to Dubai and New York-JFK.