The oversized red neon sign of Katz's Deli lights up the Lower East Side, a beacon to hungry New Yorkers. Inside the cavernous wood-panelled interior, diners chow down on plates piled high with Jewish comfort food. Behind the counter, a long line of cutters jab carving forks into metal steam boxes containing brick-red pastrami and melt-in-the-mouth corned beef. A blast of garlicky, salty, meaty steam shoots out as they stab and prod in search of the perfect piece. With the skill and speed of craftsmen, they hand-slice wafer-thin cuts of meat. Regulars, brandishing dollar bills to ensure they get the best cut, sample three or four meats before selecting the one they want.

In Katz's, site of the infamous faking scene in When Harry Met Sally, the food is enough to bring on a culinary orgasm. A fierce-looking man presides over the hot sausage plates. Waiters dart across the floor, carrying trays groaning under the weight of food.

Opened in 1888, when the Lower East Side was home to a large Jewish community, Katz's bills itself as the oldest operating Jewish Deli in the world. It has fed everyone from Sarah Jessica Parker and Spike Lee to Bill Clinton and Jimmy Carter.

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Though Katz's is besieged by tourists during the day, at night it is still home to a lively local clientele, including Joyce and Jacob Weisz. "New York has changed but Katz's is always the same. The service, the staff, the banter, the food," says Joyce. "I've been eating the corned beef sandwich here for 50 years and it tastes the same as it always did." The couple first came to Katz's when they were courting. "I'd save up all week to bring Joyce here," recalls Jacob Weisz.

The Jewish deli is as iconic a part of the New York landscape as the Empire State Building and the Statue of Liberty. But though in a handful of establishments you can still find enough knishes, kishkes and kreplach to keep the New York winter chill at bay, these culinary institutions are under threat. In 1931 there were 1,550 Jewish delis in New York City; today just two dozen remain. They are the victim of spiralling rents, the dispersal of Jewish communities, a decline in people keeping kosher and the rise of healthy eating. With a menu heavy on red meat, fat, salt and carbs, Jewish food is nothing if not artery-clogging. Gribenes – chicken skins fried in chicken fat – is a sumptuous mouth sensation, though less kind to the waistline.

"It's hard work, the deli business. You have to be prepared to get your hands dirty," says Katz's co-owner Alan Dell. "A lot of people who ran mom-and-pop delis wanted their children to have a better life so they sent them to college and the family tradition died out."

Once upon a time, you couldn't walk a block in the Lower East Side without being hit by the meaty aroma wafting through the doors of one deli or another. "You had this concentration of Jewish workers who needed kosher food and these pickled and preserved foods were cheap, filling sustenance," says David Sax, a lifelong deli lover and author of Save the Deli. Today there is only Katz's left in what was once a thriving immigrant community. The delis, Jewish tailors and other immigrant businesses have been swept away by gentrification to make way for an influx of trendy bars and designer boutiques.

After noticing the same trend in his native Canada, Sax got the idea for his book. He says: "I spoke to lots of deli owners and they all had the same story; the deli was in peril."

Sax's research took him coast to coast across America, through Canada, London, Paris, Krakow and Brussels. "Each place I went to, the deli had been strongly influenced by the community it existed in," he says. "New Yorkers have this idea that good delis don't exist outside the five boroughs but it's not true. There are great delis everywhere. The Jewish delis in the UK are as good, and in many respects better, than anywhere in the world, including New York."

Sax kept a blog, www.savethedeli.com, during his trip. He also took up jogging to counteract the unavoidable damage eating in up to four delis a day would do to his weight. Everywhere he went, deli owners pulled up an extra table and brought out trays of food for him to sample. Mishmosh, p'tcha, pickled tongue, brisket, kasha varnishkes, tzimmes, speck, chopped liver, blintzes with apple sauce ...

"Sometimes they'd get really offended if I couldn't eat it all," says Sax with a chuckle.

Delis sprang up wherever there was a concentration of Jews. In New York, they thrived in the theatre district, the garment district and the Lower East Side. They were a mishmash of influences from Poland, Romania, Germany, Hungary, Russia and beyond but New York Jews made the deli their own. Hubs of stodgy comfort food and crackling conversation, they became the place where generations of writers, theatrical agents, tailors and the rest would go to kvetch (grumble) and gossip.

Come election time, the deli becomes a powerful symbol as politicians chow down for the cameras. Presidential candidate George McGovern committed career suicide during his 1972 campaign against Richard Nixon when he walked into a delicatessen in the Lower East Side and ordered a "kosher hot dog and a glass of milk", breaking the basic kosher rule of not mixing meat and dairy. Nixon easily won New York.

Today only a small fraction of American delis are kosher. The costs of being certified and ensuring all products comply, coupled with the fact that fewer Jews keep kosher these days, has made it a luxury few can afford in today's climate.

Another factor in the deli's demise is the low margins of its star attraction: the meat sandwich. "You might make 10 per cent profit because the meat is so expensive and there's so much of it," says Sax. Shrinking portion sizes is not an option. "This is the food of poor immigrants. To have a full stomach was the best thing in the world," he adds.

In the early days of the deli, before refrigeration, everybody cured their own meat, made their own pickles, and bought bread from a neighbouring bakery. Now, most American delis order products in, and many recipes grandma used to make have been dropped from the menu to reflect changing tastes.

In Jewish delis in the UK, traditions that have fallen out of fashion in the US are still rigorously upheld. All the delis Sax visited in London continue to slice meat by hand – compared with just four in the whole of America. Good meat, a deli connoisseur will tell you, should be so tender that it will fall apart unless cut by hand. And while most American delis buy in their meat products, in the UK they continue to be pickled in barrels in the store. "The places I visited in the UK were very much rooted in their Jewishness in a way they aren't any more in the US," says Sax.

In New York's Upper West Side, the dining room of Barney Greengrass, founded in 1908, looks like a museum piece. The tables are formica, crockery is chipped and the walls look as if they haven't seen a fresh coat of paint since the old ladies at the next table were in kindergarten. But all this is part of the cosy, careworn charm. A few ageing regulars shoot the breeze but otherwise it's quiet on a weekday afternoon. Billing itself as "the sturgeon king", Barney Greengrass is also famed for its white fish, salmon and sable. Over the years regulars here included Groucho Marx, Irving Berlin, Al Jolson and Alfred Hitchcock who reputedly had 10lb of fatty sturgeon flown to him in LA.

Today the waiter serves everyone in his own good time and schmoozes like a character in a Woody Allen movie. He says: "Young Jewish immigrants are more assimilated, they have less of a connection to the food. They eat deli once a month or on special occasions, not every week like we used to."

Abe Lebewohl, the original owner of the famous Second Avenue Deli, used to joke with customers "my food will kill you". In 2006, spiralling rents forced the Second Avenue Deli to close. Its reopening on East 33rd Street, after a two-year absence, has been hailed by some as a sign that the deli will rise from the ashes.

Other old-timers include the Stage and Carnegie Deli, where the theatrical agents meet to swap stories in the Woody Allen film Broadway Danny Rose. The Carnegie offers a sandwich named after the director, consisting of "lotsa corned beef and lotsa pastrami" which weighs in at only slightly less than the great man himself.

But while the food takes centre-stage, the experience of eating deli is about more than what you put in your mouth. "It's about tradition, nostalgia and schmoozing," says Second Avenue Deli regular Sylvie Berger, tucking into a bowl of steaming matzo ball soup.

In the past every deli had its shtick and the service could be gruff. That too has changed. "You wouldn't stay in business if you abused your customers like that these days," laughs Katz's Alan Dell nostalgically. Despite the changes, Dell is optimistic: "A world without delis would be like a world without Italian restaurants. It just ain't gonna happen."