Contestants on the panel show were asked which of the above items were vegan, and were shocked when host Sandi Toksvig said none of them are.
"It's the same reason as honey," said Toksvig. "They can't exist without bees, and bees are used in, let's call it an 'unnatural way'.
"Because they are so difficult to cultivate naturally, all of these crops rely on bees which are placed on the back of trucks and taken very long distances across the country.
"It's migratory beekeeping and it's unnatural use of animals and there are lots of foods that fall foul of this. Broccoli is a good example. Cherries, cucumbers, lettuce. Lots and lots of vegan things are actually not strictly vegan."
But The Vegan Society disagrees with QI's branding of these items as non-vegan. "Vegans avoid using animals as far as possible and practicable," spokesperson Dominika Piasecka told Plant Based News.
"We are aware that many forms of farming involve indirect harm to animals but it is unfortunately not possible or practicable to avoid the destruction of other animals in most farming at this time.
"However, we do not consider that just because it is not possible to avoid one hundred percent of the cruelty, suffering and exploitation to animals that we should not bother at all.
"Vegans make a huge contribution to the reduction in suffering and death caused to animals and we would welcome any changes made to farming practices that support this."