Mark and Jermaine were shot dead by the Metropolitan Police in the north London borough in August 2011 and December 2015.
Pamela, Mark's mother, told Socialist Worker, "It's is not just about Mark—they're getting away with murder.
"They're dying the same way by police, the people are supposed to be protected by them."
Pamela added, "It's been a long time since Mark's death, but nothing seems to be happening.
"We're going to keep on fighting for justice."
Mark was unarmed, but the officer was cleared of any wrongdoing. A jury upheld the officer's "honest held belief" that Mark was armed and aiming a gun when he shot him.
Margaret, Jermaine's mother, told Socialist Worker, "There is no death penalty in Britain, but the police are doing it on their 'honest belief'.
"They should go to prison."
The anniversary of Mark's death comes after the police killings of three other black men this summer.
In nearby Hackney in east London Rashan Charles, a 20 year old, died after being chased by the police last month. Similarly Edson Da Costa died after being arrested Newham in east London in June.
Margaret said, "The one down the road was just a boy, his mother's heart must be broken just like mine was.
"Every one of the families that have been affected have got to stick together and keep fighting for justice."
Pam and Margaret joined a march of up to 100 people from the Broadwater Farm Estate to Tottenham Police Station.
Chants of "Who killed Mark Duggan—police killed Mark Duggan" rang out through the estate.
At the rally speakers included local campaigner Stafford Scott and Becky Shah whose mother died as a result of the 1989 Hillsborough football disaster.
Six years on people are determined to get justice for Mark and all those who have died after coming into contact with the police. As Adam, one of the marchers, told Socialist Worker, "This is unfinished business.
"After Mark Duggan was killed people were told that there was going to be change, but the families are still not having their voice heard."