Excluding 'don't knows' You Gov found that 48% of people wanted large stores to be open for longer on Sundays.
The government is proposing to let local authorities decide their own Sunday trading laws.
Currently large stores can only open for six hours on a Sunday but the government's facing fierce criticism from the Church and other Christian organisations on their plans to scrap that rule.
The poll found that 25% thought the proposals were a very good idea, 23% a fairly good idea, 13% a fair bad idea and 20% a very bad idea.
Around 19% of people were not sure.
Ministers claim extended trading hours will help boost the high street. The poll found that the majority (43%) of people agreed.
However the poll did discover that the overwhelming majority of people (58%) were concerned that smaller local shops would lose out if bigger stores were able to open longer on Sundays.
It also found most people (48%) agreed that longer opening hours would be detrimental to family life and the majority thought it would be bad for employees.
Meanwhile 38% of people wanted supermarkets to be open longer on Sundays but 56% said any change in trading hours would not affect their shopping habits.
