Emergency services were called at around 4pm following reports of the structures collapse at the site in Oxfordshire.
Demolition contractor Coleman and Company had been prepping the building to be destroyed in the coming months.
More than 40 people were treated at the scene for dust inhalation.
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Five people have also been taken to hospital, two with serious injuries.
A major search operation is now underway for the three missing people.
In a statement, Coleman & Company said: "We can confirm that shortly after 4pm this afternoon part of the boiler house at the former Didcot A Power Station site in Oxfordshire collapsed.
"It is with great sadness that we understand that there has been one fatality, five people have been taken to hospital and three people are currently missing and unaccounted for. Our thoughts are with the families of all those involved in this tragedy
"We are working with the emergency services who are currently on site to locate those missing and understand the cause of this collapse."
(LM)
