The James Bond star's Scottish lilt and the TV chef's British accent were favoured over the voices of Hollywood stars such as Angelina Jolie and Johnny Depp.
Connery also topped the list for the accent that most men wanted to have, while most women voted Absolutely Fabulous star Joanna Lumley as having the ideal voice.
"Upper-crust tones are clearly what women desire for themselves, while men tend to aspire to the smooth and rugged action-man vocal style," said Tony Robinson of Spinvox, who commissioned the online poll.
Comedian Joe Pasquale was voted as having the most annoying male celebrity voice, narrowly beating David Beckham and Prime Minister Gordon Brown, who came second and third respectively.
Janet Street-Porter was named the most annoying female voice, beating Amy Winehouse into second place and Katie Price into third.
A total of 1,966 adults were polled online in December by Spinvox, a company which converts mobile phone voice messages to texts and emails.