Since the early days of moving pictures, a favourite staple of Hollywood has been to imagine New York city being invaded by nasty creatures that hide in dark corners. The Beast from 20,000 Fathoms, one of the first monster films, starred a dinosaur that emerges from hibernation to crunch its way up Fifth Avenue, spreading mayhem in its wake. Then, of course, there was King Kong perched atop the Empire State Building. More recently, the zombies roaming Washington Square in search of Will Smith in I Am Legend were classics of the form, as were the aliens who lopped off the head of Lady Liberty in Cloverfield.

Having been raised on all these celluloid enactments of non-human invasion, you would have thought that New Yorkers would be pretty unfazed when the real thing happens. But, judging by the increasingly hysterical headlines that have been blasted across the pages of the New York Post in the last few weeks, that's not the case.

For the truth is that the city really is under attack this time, and its residents are starting to panic.

Today you can go to the cinema in Manhattan to be scared out of your wits by images of New Yorkers being eaten alive by monsters and, at the very same time, you can yourself be eaten alive. That's what happened to several cinemagoers last month at the AMC Empire 25 in Times Square, and, again, at the AMC theatre in Harlem.

The monsters in question may lack the muscle structure of King Kong or the fire-breathing capacity of The Beast, but boy do they bite. Cimex lectularius, the common bedbug, is on the march, steadily extending its reign of terror across the five boroughs and onwards to cities across America.

The invasion has already claimed some of the biggest names in the city. Last month, the mammoth Niketown store on 57th Street was shuttered after bedbugs were discovered, and the New York headquarters of Google was also forced to admit it had an infestation after one of its employees Tweeted on the subject. "Jeepers," she posted, "I am not immune to the bedbug panic. Bedbugs have been found at work." (The Twitter feed rapidly disappeared.)

Bloomingdale's also had a visitation, though, being Bloomingdale's and a cut above the rest, the store made clear it had found just one insect in its 59th Street store, which it dispatched post-haste. The fourth floor of the Wall Street Journal's Sixth Avenue headquarters was also struck. The Guardian offices in 27th street have so far remained delightfully free of the blighters, though as I'm typing this I appear to be breaking out in psychosomatic itches.

Earlier victims of the epidemic include Abercrombie & Fitch, teen's clothing store Hollister, Victoria's Secret, posh Manhattan condos, Broadway theatres, the headquarters of the chief Manhattan prosecutor – no chance for a plea bargain there – and, in a neat link back to King Kong, the Empire State Building. The problem has got so bad over the last 12 months, with some 24,000 recorded complaints of infestation, that mayor Michael Bloomberg has set up a bedbug advisory board and is soon to appoint a bedbug tsar.

It's all very New York. One of the great modernist cities, where people from around the world congregate to share in its energy and lust for new thinking, is in the grip of an epidemic of wingless, flightless, grubby insects. And the results are not pretty.

Here's what happened to Annie Weinstock, who works for the Institute for Transportation and Development Policy in New York. In May, she returned from a year's trip to Africa and, after a few weeks sleeping on her sister's couch, found an apartment to rent in Brooklyn.

At 2am on her first night in the new flat she woke up. (Health warning: If you are phobic to insects, you may find the next bit distressing. Please ensure you are seated before reading on.)

What woke Weinstock up was that she could hear something moving around in her ear. Yes, a bedbug in her ear! "I couldn't actually feel anything because they are so light, but I could hear it jumping around."

It doesn't get any better.

"I put on the light and I immediately saw something in the bed, I smashed it and there was blood everywhere!"

Weinstock retracted that statement as soon as she had made it on the grounds that it was exaggeration. There wasn't, she corrected herself, "blood everywhere", but there was a red stain about the size of a dime where the bedbug had been, though I'm not sure that's much of an improvement.

Without even searching she could see two or three other bedbugs on the bed. "They were very big because they were bloated with my blood."

So what did she do?

"I freaked out."

She left the bedroom and spent the rest of a fitful night in the living room. Next morning she had another look at the bed and there were at least seven bedbugs on it. She called an extermination company and they found the insects all over the apartment: in and under the bed, in the closet, in the curtains.

At first, she couldn't feel the bites at all. That's a common reaction, as it takes a while for the body to sensitise itself to the bedbugs' juices. But four days after that first night, she started itching. She had blotches all over her neck, shoulders, arms and face, about 25 in all, and they kept on itching for three weeks. "The bites were so itchy it was painful. I just sat at my desk at work and doused myself every 10 minutes with anti-itch gel."

Weinstock, unsurprisingly, couldn't bear to move back into the apartment, despite it having undergone a pesticidal equivalent of the blitzkrieg. "I realised I had been rather traumatised. I still think about it, and sometimes wake up in the night and have to check my new bed to see if there are any there."

So what are these creatures and what is it about them that makes them so panic-inducing? Bedbugs are of the insect family Cimicidae. They are oval in shape, flattish and grow to about the size of a small apple seed. They are light in colour and hard to detect, though become dark red after they have fed on your blood. That's the fun part. They come out at night like ghouls and gorge on your blood when you are deeply asleep, for up to five minutes.

Then they scurry back to their hiding places in bed frames, box springs, carpets, under floorboards, in cracks in the wainscoting, behind wall hangings, in clothing, in the electrics – you name it. They can live for up to a year without feeding, which makes them very hard to eradicate.

Richard Cooper is a director of BedBug Central, an educational website and prevention company that last week organised a nationwide "summit" in Chicago, attended by about 400 of America's top bedbug experts. He also sits on Bloomberg's advisory board.

Over the last 10 years he has got to know the bloodsuckers very well, watching them multiply from virtually nothing to take hold of New York, and now other US cities such as Philadelphia, Detroit and Cincinnati. So what does he think of them?

"I'm fascinated by them. I respect them. They have extraordinary strategies for succeeding."

One reason often cited for the resurgence of the pest is the banning of the toxic chemical DDT, with which they had previously been brought under control. But Cooper believes the main cause of their success today is human ignorance. People are unaware of what to look for and miss the early signs, allowing the bedbugs to establish themselves and spread throughout a dwelling. Part of the problem is the assumption that infestation is confined to poor neighbourhoods with dirty and crowded living spaces.

Wrong, says Cooper, who is taking a PhD in the impact of bedbugs on low-income communities. The bedbug invasion began among the wealthy and middle classes, where frequent international travel for work and/or leisure allowed the insects to penetrate salubrious homes via luggage.

It is only in the last few years that the insects have begun to encroach on poorer areas of New York, with devastating results. Families there often can't afford the cost of extermination, and that further aids the bugs' march across the city.

Kate Lewis, a magazine editor in Brooklyn, knows how expensive dealing with an infestation can be. She spent about $3,000 (£1,900) after she discovered the insects a year ago – about $2,000 to exterminate them and about $1,000 on new clothes, bedding and so on.

Her family had been staying in a rental holiday house in Florence, and when they got back to Brooklyn her husband Jacob began unpacking the suitcase on their bed. Big mistake. That's one of the easiest ways to allow the monsters into your life. Jacob actually saw a bedbug crawl out of the luggage and on to the bed.

He ignored that, but a little later they saw another one so they tore the bed apart and found at least five bedbugs in it. "There's a traumatic moment," Lewis says, "when you kill one and realise they are full of your blood. It's upsetting. I'm not that bothered by insects, unlike Jacob, but they eat you! They are kind of sweaty-looking and glistening, and you think to yourself, 'They are going to do me in.'"

They acted swiftly, bagging up all their clothes and all the fabric material in their three-storey house and putting it in the basement, then leaving the house immediately. Even after all the money they spent, they lived for much of the last year in terror, waiting to see whether the bugs would make their nocturnal return.

A further problem is the stigma attached to infestation. A Manhattanite I spoke to made the point elegantly for me by asking to be anonymous. Four months after his bedbug saga he still fears the opprobrium of victimhood.

"There's a definite stigma around it. When I had bedbugs, people wouldn't come round to my apartment. You could understand that, but they also wouldn't invite me round to their places, as though I was a carrier or something."

The pest control company Usbedbugs is so aware of the sensitivities that it sends out its products in plain brown cardboard boxes, with no mention of the nature of its business on the labelling.

That suits the bedbugs well. People who have suffered attacks keep silent for fear of the consequences, thus failing to alert neighbours to the danger and, in turn, allowing the bedbugs to advance undetected. And so the shiny creatures proceed, slowly, steadily, bloodsucking their way across the city and spreading misery in the form of itchy blotches and panic in their wake. It's an interesting twist on the classic New York invasion storyline. In the Hollywood movies, the monster is always finally defeated. In this real-life battle of Cimex lectularius versus Homo sapiens, a happy ending should not be taken for granted.