Almost half of those questioned said the darker evenings would leave them "depressed".
More than one in four feared being mugged or suffering an accident.
These fears encouraged more than four in 10 to remain indoors. Almost a fifth said they would participate in more sports if they had an extra hour of daylight.
The survey, conducted earlier this month, also found that one in five struggled to pay the winter heating and lighting bills as fuel prices continued to rise.
Richard Al-Dabbagh, the head of insurance marketing at Santander, which commissioned the survey, urged people to overcome their fears of the long nights.
"Darker evenings can lead to a higher incidence of crime and accidents," he said. "However, they are no reason to stay indoors or limit our activities."
Last year a study from the London School of Hygiene and Tropical Medicine suggested that child obesity could be reduced if the clocks did not go back in the winter.
The government had agreed to support a Private Members Bill, Rebecca Harris, the Conservative MP for Castle Point, which would have led to a detailed official study being carried out on the impact of the change.
Under the measures, which eventually failed to get support in Parliament, the British time zone would permanently have been brought forward in both winter and summer, putting Britain in the same time zone as most of continental Europe.
Supporters argued the permanent shift forward to "double summertime" would allow most people an extra 235 hours of daylight after work every year.
It would have also meant lighter evenings, with sunset in midsummer after 10pm in many parts of the country.
They also argued that putting the clocks forward permanently by an hour would boost the economy, help the environment and give people hundreds of hours of extra daylight every year.
But mornings would become darker, especially in Scotland, where the change has long been opposed.
David Cameron had indicated that he was prepared to consider the change as long as it was supported by all of the country.
A Department for Business spokesman said last night: "The Prime Minister has made clear a change about permanently moving the clocks forward should only occur if there was UK wide consensus.
"The Government would not expect to make any change if there was clear opposition from any part of the country." Britain has experimented with clock changes before.
From 1968 to 1971, summertime applied throughout the year in an arrangement known as British Standard Time but after complaints in Scotland and northern England, MPs voted to end the experiment.