The celebrity-driven trend for bulldogs and pugs has seen a surge in the number of medical procedures carried out on the pets.
The Royal Veterinary College (RVC) said many buyers are unaware that the flat-faced dogs can suffer serious breathing problems as a result of being bred to look "more attractive".
Operations to reduce the distinctive folds, which threaten their airways and sight, have surged five-fold over the past four years, the central London college reported.
Demand for the dogs has dramatically increased as a result of a number of high-profile celebrities favouring the breeds, including Made In Chelsea star Millie Mackintosh, singer Miley Cyrus and footballer David Beckham.
Dr Gert ter Haar, the RVC's senior lecturer in soft tissue surgery, said: "Some dogs have such excessive skin folds that they fold over their nose and eyes and impair their breathing.
"It can also lead to very severe inflammation of the skin. It's very uncomfortable and can really reduce their quality of life.
"Most people don't like it when you take out the folds because it's one of the things that is distinctive about pugs and bulldogs but from a professional perspective I don't agree with that.
"These are very specific problems that are really a result of breeding, making the skulls shorter and shorter for more attractive pets as demand grows.
"We've always bred dogs to look a certain way or perform a certain function for people and that is fine, but it's our job to make people understand that there is a limit."
The college has set up a specialist clinic to collect and analyse data taken from dogs that require surgery, in the hope they can offer advice to breeders about how to avoid the problems.
Mr ter Haar said he hopes the surgery will no longer be required within 10 years as a result of the research.
French bulldogs are currently the most popular breed of dog in England, with the number of owners registered with dog welfare organisation the Kennel Club rising from 360 in 2004 to 6,990 in 2013.
The number of pugs rose from 1,675 to 8,071 in the same period.
Dog welfare organisation the Kennel Club urged buyers not to take dogs with exaggerated features.
A spokeswoman said: "The number of people buying pugs and French bulldogs has grown astronomically in recent years, often driven by celebrity influence, which explains any increase that some vets might see of these breeds in their surgeries.
"Many of these dogs will be bred well but unfortunately there are still too many breeders who are cashing in on the surge in demand and breeding for exaggerated traits that are detrimental to their dog's health, which is why we always urge puppy buyers to see the pup with its mother and father, so that they can avoid pups from those dogs with unhealthy exaggerations."
She added that as a result of the popularity of pugs and bulldogs, many native British breeds, including English setters and Pembroke Welsh corgis are "at risk of disappearing from our streets".