Derbyshire police said they believe the fire was started deliberately when petrol was poured through the letterbox last Friday.
Assistant chief constable Steve Cotterill said the seat of the fire was below the letterbox at the front door of the house. Investigations showed the accelerant was petrol.
"What I can tell you is that the fire was started deliberately," Cotterill told reporters.
Results of post-mortem examinations revealed that the five younger children