The idea is the latest to emerge from the Tories' Quality of Life group, headed by millionaire eco-warrior Zac Goldsmith and former environment secretary John Gummer.
The report suggests such a move might encourage shoppers to use their local grocery stores, and so curb the multiples' growing might.
"There is a huge imbalance of power on Britain's high streets," Goldsmith said. "These proposals could help to balance out the playing field, and tackle the growing problem of the ghost town phenomenon."
Encouraging people to ditch their cars would also be better for the environment, he added.
Association of Convenience Stores chief executive James Lowman welcomed the report's recommendations. "The current system of car parking charges is inherently unfair on retailers trading in and around town centres," he said.
The report also recommended a separate planning use class order for small-scale retailers and service providers, as well as a ban on below-cost selling.