The family, from Sittingbourne in Kent, are now pursuing a negligence claim against Network Rail with law firm Bolt Burdon Kemp.
“A lovely family day out ended in absolute disaster for us,” the boy’s father said.
“I am confident our little boy wasn’t doing anything he shouldn’t have been on the escalator. We were right next to him and it was such a frightening experience to see him suddenly trapped like that.”
He added: “Since the incident, our little boy has been really suffering and is now completely terrified of going near any escalators or lifts. We felt it was important to speak out about what happened to us, so parents know to be extremely vigilant when travelling around London.”
He added that a passing doctor had assisted the family with the boy’s injury.
Ben Pepper, a senior associate at Bolt Burdon Kemp, said Network Rail has denied liability and that the company has said the escalator was not unsafe or faulty.
“This family’s harrowing ordeal really shines a spotlight on the dangers of escalators and particularly the dangers of travelling with children,” he said.
“It’s really disappointing to see Network Rail deny liability for this issue and we hope, through our ongoing legal investigation, we can identify those features of the escalator that were unsafe and ensure this tragedy doesn’t happen to anyone else.”
A Network Rail spokesman said: “The safety and wellbeing of our passengers is always our number one priority and our thoughts are with the young boy and his family at this very difficult time.
“Everyone in Network Rail and particularly the team at London Bridge station are saddened by this incident, however, while the case is ongoing, it would be inappropriate for us to comment any further at this stage.”