The men were arrested last year outside a branch of the Iceland chain, the Guardian reported. The charges only became public Tuesday when the newspaper reported the cash, causing a massive backlash.
The Crown Prosecution Service announced Wednesday the charges were being dismissed. Paul May, Jason Chan and William James were charged under the 1824 Vagrancy Act.
Iceland's chief executive, Malcolm Walker, requested the charges be dropped.
The men were arrested in October in London's Kentish Town neighborhood. A passerby who saw them climbing into a wall to get into the enclosed yard where Iceland's trash bins were located called police.
Police said they were caught leaving the area with 33 pounds ($50) worth of food, including mushrooms, tomatoes, cheese and Mr. Kipling cakes.
May said he did not see taking good food that would end up in a landfill to share with his housemates as a crime.
"Did we have dishonest intent when we jumped into the yard at Iceland to retrieve what was in the bins? No, we didn't," he said. "A dishonest action would be wandering into a store and filling your pockets with what is on the shelves. We didn't do that."