Kaden Reddick, whose parents are from East Kilbride, suffered serious head injuries in an incident involving a store display barrier in Reading’s Oracle shopping centre, police said.
He was taken to the Royal Berkshire Hospital after the incident at 4.15pm on Monday but was pronounced dead.
The Sun reported that a worker for the high street chain said bosses had ordered the removal of till display units from stores.
A spokesman for Topshop said it was “not making any further comment” beyond a statement issued on Tuesday which said: “The Topshop board together with thousands of staff are deeply saddened by the horrific accident that occurred in our Reading store yesterday afternoon.
“All our thoughts are very much with the family at this difficult time.
“We are thoroughly investigating all the events surrounding this extremely sad situation.”
Kaden’s parents changed their Facebook profile pictures to feature their son. Father Ian Reddick posted: “Love you my little man, it’s hurting so much.” Mother Lisa Cooper Mallet replied: “I feel you.”
Friends, family and well-wishers have offered support.
Anthony Mallett posted: “It’s unbelievable to think how quickly life can change, how cruel life can be. Our love and thoughts are with Lisa Cooper Mallett. We love you and will always be here for you.”
Aly Mallett wrote: “I wish I could just be there now to give you the biggest cuddle ever, love you all lots and thinking of you all.”
Trish James said: “Love you guys, the worlds going to miss you wee man and the amazing things you would have achieved in it.”
Thames Valley Police said on Tuesday that Kaden “suffered serious head injuries after an incident involving a store display barrier”.
Detective Superintendent Paul Hayles said: “We are supporting the boy’s family to assist them at this very difficult time.
“We continue to investigate the circumstances surrounding this death.
“A scene watch is in place at the Topshop store and is likely to be in place for some time.
“Detectives are now working with the local authority and the store owners to gather all of the information on how this incident happened.”
The store was closed on Tuesday as investigations continued.
Police staff could be seen inside the shop, and bunches of flowers were left against the closed shutters.
One card, which was unsigned, read: “RIP little man.”
Reading Borough Council said: “As the enforcing authority for health and safety within retail premises, we will be working closely with the police, who are at present leading on the investigation.”
The tragedy comes after a four-year-old boy was killed when an 18st mirror crushed him in a shop changing room at Bicester Village in Oxfordshire in June 2013.
Austen Harrison died from severe head injuries when the 7ft mirror, which had been left standing free rather than being attached to a wall, toppled on to him at a Hugo Boss pop-up store.
An inquest concluded the mirror should have been fixed to a reinforced wall, and coroner Darren Salter called the incident “an accident waiting to happen”.
The designer brand was fined £1.2 million after admitting breaching health and safety regulations.