The poll, commissioned by the Press Association, also revealed that 1 in 8 OAPs said they planned to stop using parts of their homes in the cold weather in an attempt to keep energy bills down.
Almost two-thirds of those surveyed (64 per cent) said they had to wear extra layers of clothing in an attempt to stay warm, while a fifth said they planned to cut back on other areas of spending so they could afford to heat their homes.
Two-fifths of the respondents added that they would struggle more than in the past to pay their energy bills this winter.
Paul Green, director of communications at Saga, said: “As we head into the cold winter months, spiralling fuel costs are striking fear in the hearts of some, but not all, pensioner households.
“For some, the fear could mean they won’t turn on their heating on, and in so doing, risk their own health and welfare.”
Jane Vass, head of public policy at charity Age UK, said: “High energy prices, along with poorly insulated homes are some of the factors that cause cold homes – a major cause of excess winter deaths.”
She added: “Long term we strongly believe that the only sustainable solution is investment to increase the energy efficiency of our housing stock so cold homes become a thing of the past.”