Huge price spikes are also leaving houses using heating oil vulnerable to theft.
Suffolk Police says several properties in Woodbridge have been hit by criminals trying to source the fuel.
John Birchall, who lives in Hollesley, on the east Suffolk coast, checked his tank last week to find out his heating oil had been stolen, and that of his neighbour.
The commercial property surveyor estimates about 800 litres (175 gallons) was taken from his tank, which holds about 1,225 litres (270 gallons).
Birchall relies on the oil to heat his home and water, supplemented by wood burners and solar panels.
His supplier has already refilled the tank – and he has increased its security.
“Historically, I’ve paid as little as about 20p a litre during Covid, generally between 50p and 60p a litre – and this time it was £1.30 a litre,” he says.
“Values are so high now they sell it on very quickly; these are the unintended consequences of the war in Iran.”
Officers are urging people to make their tanks less visible and be wary about rogue traders selling oil at a discounted price.