New research by Whatcar.com has revealed more than a quarter (26%) of motorists would feel comfortable enough being driven in an autonomous car that they would sleep while travelling.
Other activities passengers said they would be comfortable doing while being driven in a car with autonomous technology included talking to fellow passengers, browsing the web and watching TV.
Despite motorways being the highest-speed roads in the UK, almost a third (32%) of drivers said driving on a motorway would be the best time to have a self-driving car.
City driving was also a popular option, cited by 18%, however, relinquishing control during a traffic jam was the most appealing option for nearly half (49%) of respondents.
Yet the survey found the majority of drivers still do not trust autonomous technology, with nearly half (45%) saying they find the technology very unappealing. What's more, over half (51%) said they would feel unsafe or very unsafe in a self-driving car.
The biggest reservation among drivers was that an autonomous car would not be able to avoid an accident, cited by just over a third (34%).
A similar amount (30%) of respondents said losing the enjoyment of driving was their biggest worry.
Whatcar.com editorial director, Jim Holder, commented: "It's clear that autonomous cars have a way to go before the concept is truly adopted by the motoring public."
Autonomous safety technology is already on board more than half of new cars sold, with manufacturers including Ford and BMW working on driverless vehicles.
Would you feel comfortable sleeping in a self-driving car?