The 17-strong group, which includes three Olympians, have served a Letter Before Action alleging “systemic physical and psychological abuse” upon children as young as six, according to the PA news agency.
The letter sent by law firm Hausfeld says the survivors were aged between six and 23 at the time of the alleged abuses, which included "widespread inappropriate use of physical force" by coaches and enforcement of "baseless" weight management techniques.
An independent review commissioned by UK Sport and Sport England and led by Anne Whyte QC to look into complaints of mistreatment within the sport is currently under way.
Jennifer Pinches, who retired from international competition after helping the Team GB reach the final at the London Olympics, said British Gymnastics had spent too long prioritising "podiums over people".
"It is a heart-breaking truth to face, knowing the level of abuse that we and so many others were subjected to," said Pinches, who is now the community director of the Gymnasts for Change group.
"This is just the beginning of the sweeping changes that we are demanding, and the justice that we will fight for."
Gymnasts for Change campaign director Claire Heafford said: "This is not and has never been about a few bad apples, this is about decades of systemic abuse, encouraged and covered up by those at the top.
"The hopes and dreams of countless children and young adults of competing as professional gymnasts have been destroyed and their love for the sport is now shrouded in fear and suffering," she added.
The group is demanding a response from British Gymnastics which includes a formal apology, compensation and improved coaching guidelines.
In November British Gymnastics appointed Alastair Marks as its new interim chief executive, replacing Jane Allen who retired from the role in December amid allegations of bullying and abuse within the domestic sport.
The hiring came months after British Gymnastics announced that national head coach Amanda Reddin had temporarily stepped aside while complaints against her were investigated. Reddin has denied any wrongdoing.
British Gymnastics has been approached for comment.
Additional reporting by PA.