With their squishy jowls and gentle disposition, English bulldogs unseated Labradors as the Big Apple’s most popular breed in 2013, according to rankings released by the American Kennel Club (AKC) back in February — but nearly 300 of the chubby canines were surrendered to shelters in the city that same year.

The breed is a tragic victim of its success. Bulldogs have grown by leaps and bounds in popularity thanks to their family-friendly attitude, but they’re also difficult to care for — stubborn and beset by health problems — and new owners often don’t realize the challenges until they’ve already brought a cuddly pup home.

“[The English bulldog’s] year-over-year increase in popularity fuels the year-over-year increase in the number of dogs we rescue,” says Laurette Richin, executive director for Long Island Bulldog Rescue (LIBR). “In 1999, we rescued 13 dogs. In 2013, we rescued 347.”

Since certified AKC breeders can’t keep up with the demand for healthy puppies, many of the purebreds living in the five boroughs come from illegal puppy mills and overseas breeders who haven’t taken proper care of their charges — resulting in health problems that novice owners are unprepared to treat properly.

“The most common issues we see are skin, ear and eye infections, and elongated soft palates — when there’s a chunk of skin in the back of the throat obstructing the airway,” says Richin. “We’re also seeing more bladder stones and seizure disorders.”

Astoria resident Julia Maria Conway, who rescued her second bulldog, Lucille, from a Tennessee puppy mill, is all too familiar with these medical woes.

“Many bulldogs have allergies. You have to wash their folds and clean their ears on a regular basis. Interdigital cysts are common; they can have digestive issues, and bad breeding causes spina bifida,” says the 38-year-old.

As a member of the Mayor’s Alliance for NYC’s Animals, LIBR receives an alert every time an English bulldog comes through Animal Care & Control, though Richin says that most are surrendered to them directly from owners. LIBR is then left to foot the bill for their medical costs, which can easily amount to $900 a year.

To cover expenses, LIBR throws an annual fund-raiser, Beth Stern’s Bash for the Bulldogs. At the event, hosted by Mrs. Howard Stern, dog lovers can rub elbows with like-minded celebs such as Ice-T and his wife Coco, while bidding on auction items.

Last year, the soiree raked in $70,000 for LIBR and its lovable pups.

The money also helps LIBR ensure that its rescues go to homes willing to put in the necessary time, money and energy to make these animals a member of the family. According to Richin, 98 percent of their adoptions stick.

As Conway can attest, the troubles that go into owning a bulldog pay off in dividends. “If you want a dog who listens to your commands and is easily trainable, this breed is not for you . . . But overall, my Lucy is so lovable and sweet, it’s all worth it in the end.”

Beth Stern’s 15th Anniversary Bash for the Bulldogs will take place Tuesday at 7 p.m. at the Rosenthal Pavilion at NYU, 60 Washington Square S. Tickets start at $150.