Elsayed Elgammal, who runs a cart called Mando Halal Food, has a loyal clientele that lines up for his signature chicken and rice dish.

But after more than two decades on the same corner in Long Island City, Queens, he still doesn’t own his business.

He pays about $20,000 every two years to rent a license — not to New York City, but to a man who obtained the permit decades ago for a few hundred dollars and has since moved overseas.

The arrangement is illegal, but it is the only way that thousands of New York food vendors can operate, because of a longstanding limit on new permits that makes it all but impossible to get one.

“Man, it’s a knife in your heart,” Mr. Elgammal said, while listing what he could have done with the money he pays for the permit: a down payment for a home, tuition for his children, a lease on a new restaurant. “What can you do? There is no choice.”

New York has one of the largest fleets of mobile food vendors in the country, powered by waves of mostly immigrant entrepreneurs seeking a toehold in the city’s economy. But the bottleneck in the permit process has left many operating outside the law and vulnerable to exploitative schemes, even as the city has increased policing of vendors.

City officials have promised to improve the licensing system but have been slow to do so. Only 14 new permits have been issued through mid-September, more than a year after the city was required to jump-start the frozen application process, according to a city progress report reviewed by The New York Times.

The latest numbers of new vendor permits and other details about the market were included in a city report prepared in response to questions from Brad Lander, the city comptroller. The Times obtained the communication through a Freedom of Information Law request.

There are about 5,100 mobile food vending permits in circulation, in a city of 8.7 million people, because of a cap imposed in the 1980s, spurred by concerns about street safety and complaints from storefront owners.

New York is the only major city to enforce such a cap on new permits, said Robert Frommer, a senior lawyer with the Institute for Justice, a national nonprofit law firm with expertise in street vending laws.

In 2021, the City Council passed a law mandating the release of another 445 permits every year for a decade and setting new rules to prevent the reselling of cart permits, which cost only a few hundred dollars when purchased from the city. The city’s slow rollout is partly because the applications for new permits were made available nine months late. A spokesman for the Department of Health and Mental Hygiene, the agency overseeing the process, said it needed time to incorporate community feedback on the new rules, while balancing responsibilities related to the pandemic.

The department said it had already sent out applications for the remaining available permits, and that it was up to the vendors to complete them. There were nearly 10,200 vendors on the waiting list in August.

“The sheer volume of vendors on waitlists suggests there’s much more the city can do to deliver the licenses and permits mandated under Local Law 18,” Mr. Lander said in a statement, referring to the 2021 law that enacted the changes.

Despite the delay, city agencies have cracked down on vendors with and without permits. Through mid-September this year, the health department had issued 4,611 summonses against permitted food vendors — more than in the previous two years combined, according to the city’s report to Mr. Lander.

The Sanitation Department, which took the lead on enforcing street vending rules in April, reported that half the violations it has issued were for unlicensed food or merchandise vendors.

“They rush to write the tickets, they rush to call the N.Y.P.D. and Sanitation to crack down on vendors, but they are not investing appropriately to get those licenses out to help vendors formalize their business,” said Mohamed Attia, managing director of the Street Vendor Project, a nonprofit advocacy group.

Violations, which can be issued by several city agencies, can result in thousands of dollars in fines or, in some cases, confiscation of carts. The most common penalties are related to operating without a cart permit, even though many of the vendors have passed food safety training courses and have already applied for licenses, Mr. Attia said.

“We continue to implement the City Council’s expansion of street food vending to ensure that there are more opportunities for people to serve food in the five boroughs,” Patrick Gallahue, a spokesman for the Health Department, said in a statement. The rate of summonses this year is in line with prepandemic norms, he said.

At the current rate of permitting, it could take years to catch up to the demand. There were four staff members at the Health Department tasked with processing the backlog of permit requests, according to the city’s report. Mr. Gallahue said staffing was “sufficient.”

Mr. Elgammal, 62, who was born in Egypt, is relatively lucky. He qualified for one of the new cart permits that had been stalled by the delayed city paperwork.

Until he receives the permit, which requires additional paperwork and an inspection of his cart, he must rely on his borrowed sticker. He said the man he rents it from, a former New York taxi driver who lives in Egypt, flies back to New York periodically to renew the license and collect his fee.

Mr. Elgammal has little protection in the arrangement. Days after he renewed the lease in 2020, the city shut down because of the pandemic, and he had no recourse to seek a refund. Last year, when the man returned from Egypt and Mr. Elgammal paid him another $20,000, he said the man joked that he was doing him a favor by not charging for the flight from Egypt.

Many other vendors cannot even be considered for the new permits. Saraí Rodríguez, 38, has been selling Mexican antojitos, or snack foods, from a cart near Herald Square in Manhattan since 2018. But to get on the waiting list for one of the newly released cart permits, Ms. Rodriguez would need to have passed a food safety class before March 2017.

She expects that she will once again have to pay a broker up to $19,000 to lease someone else’s cart permit later this month.

“I own the cart, but it feels like it’s not mine,” she said in Spanish.

Ms. Rodríguez, who lives with her four children in Corona, Queens, said she works six days a week and makes about $4,000 a month. Living and business expenses deplete most of it: $1,700 a month for a three-bedroom basement apartment, $400 a month for garage storage of her cart, and thousands of dollars set aside, in cash, for a borrowed permit.

“My biggest American dream is to own a restaurant one day,” she said, but she hasn’t been able to save enough for storefront rent.