He suffered serious head and upper body injuries and was taken by the Kent Air Ambulance to the Royal London Hospital.
He was later transfered to Great Ormond Street where he is in a critical but stable condition. His mother is at his bedside.
Police have appealed for anyone who was in the area and saw the boy to contact them.
Spokesman Rosy Alexander said: “We understand the boy was standing by the gate when it slid back into the housing and he was unable to get out of the way in time.
“Staff from the sorting office freed him.”
She added that the boy’s mother was with him at the time but it was not known who had activiated the gates.
The incident happened at 8.30am on Wednesday.
Emergency services were alerted by a resident of the flats.
Police, an ambulance and an ambulance service community responder arrived at the scene. The air ambulance was called and landed on a nearby football field.
A police and Health and Safety Executive investigation is under way.
Det Insp Angie Hobbs said: “We would like to speak to anyone who was in the vicinity before the incident and may have seen the little boy before it happened.
Aesif is unable to comment on the serious nature of this incident being under investigation, other than to remind installers about the importance of safety ribs and beams on these types of systems.
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