"A group of people have breached the airport perimeter fence and are currently staging a protest on the northern runway," the airport said in a statement.
"Both runways are open, although there will still be delays and a few cancellations," it added.
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Around a dozen activists from a group called Plane Stupid broke through airport fencing in the early hours of Monday.
"At approximately 3:45 am officers were alerted to a number of protesters who had made their way airside at Heathrow Airport," a police spokesperson said.
Still happy on the south. Loving #climateaction #noifsnobuts pic.twitter.com/FZNqqysfKI
— Plane Stupid (@planestupid) July 13, 2015
"A small number of these protesters are believed to have chained themselves."
A video uploaded on the Internet showed several activists chained together with a police officer telling them: "You are causing severe disruption and it will be in the millions of pounds because it will take us a while to remove you."
"There are international flights now being diverted," he said.
A government-appointed commission earlier this month recommended building a third runway at Heathrow to increase capacity but the issue divides Conservative Prime Minister David Cameron's government and has sparked opposition among local residents.
Plane stupid (remember us!?) live from the Heathrow runway #heathrow #keepitontheground pic.twitter.com/QacVVsV5wI
— Plane Stupid (@planestupid) July 13, 2015
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"Building more runways goes against everything we're being told by scientists and experts on climate change," said Ella Gilbert, one of the protesters.
London's five airports form the busiest air hub in the world with around 135 million passengers a year.
Heathrow handled 73.4 million passengers in 2014, making it Europe's biggest airport by passenger traffic.
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