Brown, who is partially sighted, competed for both Britain and Ireland in paralympic events including cycling and running.
He climbed on top of a passenger jet at the airport on Thursday, live-streaming his protest via Facebook.
"I'm on top of a British Airways plane to draw attention to government inaction on climate and ecological breakdown," Brown said.
Also on Saturday, more than 100 health care workers dressed in scrubs joined an Extinction Rebellion climate protest in London, gathering outside the headquarters of the Shell oil industry firm.
The "Health March for the Planet" took place on the sixth day of the Extinction Rebellion protests, which have seen nearly 1,300 arrests made so far in the British capital.
The group has staged rallies and acts of civil disobedience in cities around the world as part of a planned two-week global campaign.
"We are meeting outside Shell because they are one of the biggest companies involved in the oil and energy industry, and they have real power to decarbonise that industry," said one protester, a paediatric and emergency doctor from Bristol named Alex Turner, according to PA.
Some of the nurses, doctors and medical students in the crowd wore medical face masks, while others carried signs calling climate change a major health issues and Extinction Rebellion flags.
PA reported that 23 people were arrested at another protest by members of the animal rights group Animal Rebellion earlier Saturday. Protesters had stopped traffic from entering a London fish market.
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