Four people were in custody while the other six were being disentangled having locked themselves together across the five-lane slip road leading to the airport, causing traffic congestion at the Europe's busiest hub.
One lane of the road, a spur off a motorway which connects London to western England, remained closed at midday on Friday, police said, adding that the airport and road network were otherwise open and operating as normal.
Black Lives Matter started in the United States as a reaction to fatal shootings of black people by white U.S. police officers.
The British arm is protesting against what it says is a disproportionate number of black people among those who die in police custody in Britain.
"To be stuck in traffic is an irritation. To be denied justice for decades is a crisis," Black Lives Matter UK said on its Twitter feed.
Other demonstrations were being held in Birmingham, Manchester and Nottingham on Friday to mark the anniversary of the death of Mark Duggan, whose shooting by police five years ago helped spark several days of rioting in Britain.