The charity, which represents Romani Gypsy, Roma and Irish Traveller communities, has sent a letter of complaint to GMP via law firm Leigh Day.
It alleges the force’s actions breached police duties regarding excessive force/battery, false imprisonment, negligence and safeguarding.
The group also argues the force may have contravened equalities and human rights laws.
The Traveller Movement said children as young as 10 were “unlawfully targeted, marginalised and racially profiled”.
The group alleges the young people were called derogatory names, “subjected to physical aggression”, separated from families and put onto trains heading to unknown destinations.
In a review of the incident, the deputy mayor found the force could have engaged with these communities in advance to avoid the order being enforced.
Ryan Bradshaw, lawyer at Leigh Day said the alleged actions of GMP were “deeply troubling”.
“Young children on their way to the Christmas markets appear to have been treated like football hooligans on a rampage,” he said.
