Ecclesiastical Insurance's claims team is treating the fire at Peterborough Cathedral last Thursday as suspected arson.
An Ecclesiastical spokesman said the fire, which was battled by more than 50 firefighters, was probably started in a stack of chairs near the choir stall.
"Initial investigations by the claims team reveal no other logical explanation," he said.
Although Ecclesiastical has estimated the damage bill at between £3m and £4m, the spokesman said it could have been worse.
He said: "The head verger called the fire brigade, who arrived very quickly to tackle the blaze.
"We believe the fire was only minutes from properly catching hold and causing a much bigger loss."
The spokesman said it would take about 18 months to restore the building.