Research by the New Economics Foundation said more than half of the 1000 people questioned wanted to buy locally grown food, with 46% saying they would always buy food grown in the UK wherever possible.
However, half were worried about the dominance of the multiples over smaller high street traders, especially the effect on traders in town centres when a supermarket opens on the outskirts of the town.
Just under half of those surveyed said they would prefer to go to a supermarket if it was in their town centre, despite the impact on other traders in the area, than drive to one outside.
Director of policy at the NEF, Andrew Simms, said: "In market economies the consumer is supposed to be sovereign. But the evidence suggests that people's preference for local produce is not being met.
"Rather than being sovereign, the market treats consumers more like the kitchen help.
"The phenomenon of Ghost Town Britain, local shops and services losing out to larger operators, has drained high streets of their vitality."