The claim is made in a new report Burger and Chicken Restaurants - UK - September 2018 by market research company Mintel.
"The biggest threat to the popularity of burger and chicken is the trend of consumers cutting back on eating meat," said Foodservice Analyst Trish Caddy.
"This is being driven by Younger Millennials who have either adopted a full-time vegan lifestyle or are simply eating more plant-based dishes.
"Operators now need to tackle this issue by offering consumers more varied choice, including vegan burgers."
Vegan and vegetarian
Mintel's analysis ties in with poll data released earlier this year, that shows how young people driving the charge towards veggie and vegan diets.
Almost 8 million British residents - around 12 percent of the population - identify as vegan, vegetarian, or pescatarian according to research by Harris Interactive for food trade journal The Grocer. The 12 percent breaks down into six percent vegetarian, four percent pescetarian, and two percent vegan.
In addition, a further one in four is set to cut their meat intake over the next year, says the survey.
According to the data, 18-44-year-olds are the most likely to have stopped eating animals.
Harris Head of Research, Lucia Juliano said: "It isn't surprising that young consumers are thinking about changing their ways.
"But the over-55s aren't so concerned - 80 per cent of them plan to make no change."