The ICM poll found 56 per cent of respondents reluctant to relinquish the controls of their car, compared to just 20 per cent of those who would.
The findings follow announcements from companies including Google, Ford, Mercedes Benz, Audi and Volvo that they are investing in developing driverless cars.
The poll showed women were more wary of the new technology, with 61 per cent saying they wouldn’t use a driverless car, compared to 50 per cent of men. Thirteen per cent of 55 to 64-year-olds backed driverless cars, compared to 31 per cent of people aged 25 to 34.
In a statement, Philippa Oldham, head of Transport at the Institution of Mechanical Engineers, said: ‘Autonomous vehicles would be a huge leap forward. Much of the autonomous technology - such as automatic parking - is already making today’s cars safer, greener and more efficient. We certainly welcome any investment made which may help to improve and develop vehicles.
‘However, these results show that although the technology is developing quite rapidly, the biggest hurdles these companies face will be convincing people to hand over control of their vehicles to a computer.’
In December 2013’s National Infrastructure Plan the government proposed making the UK a world-leading centre for the development and testing of driverless cars, creating a £10m prize fund for a town or city to develop as a testing ground for driverless cars
Driverless cars use techniques such as radar, GPS, and computer vision to sense their surroundings and control the vehicles navigation path. Google claims that its prototype vehicle has achieved more than 300,000 autonomous-driving miles.