A total of 82 percent of respondents said they would like only people living in the UK to receive the payment, while 49 per cent believe the allowance should be means tested.
Consumers also thought disabled people (60 per cent) and lower income households (52 per cent) should qualify for the benefit too.
Two thirds of consumers said they think people should be allowed to opt out of receiving the winter fuel allowance – an option not currently available.
The research also highlighted that less than half (41 per cent) of people do not know how much the allowance is – £100-£300 a year – while only 18 per cent were aware anyone born before 5 July 1951 is eligible.
Ann Robinson, director of consumer policy at Uswitch, said: “Our research shows overwhelming support for the allowance to continue, but a growing recognition that payments could be better targeted at those who actually need the extra help.”