The same proportion also said that patients who regularly miss GP appointments should only be allowed access to a GP through a turn-up-and-wait system.
The findings could impact on the next round of GP contract negotiations because the government is to use feedback from the sessions to inform policy.
The event at Downing Street was attended by 60 members of the public. It followed a series of similar sessions across England.
Participants were hand picked by the pollsters Ipsos MORI to provide a representative cross-section of society.
GPC deputy chairman Dr Laurence Buckman, who voluntarily offers emergency Saturday surgeries, was sceptical of the findings, but said the GPC would be happy to talk to the DoH about creating a directed enhanced service (DES) for opening weekends or evenings.
'When you ask patients if they want longer hours, they generally say "no".
'Because this was a government think tank, the questions were probably biased and designed to get this answer,' Dr Buckman said.
He pointed out that the DoH was convinced that walk-in centres would provide better weekend care than GP practices, and had pushed the change through.
'If it wants to talk about DESs, we would be happy to talk. But if it wastes options like that it has to provide the facilities and funding - we would have to pay staff a lot more to come in at night or over the weekend.'