Queen of the underworld: Mary Beard is bringing the ancient city of Pompeii to life in a BBC documentary

Around lunchtime on 24 August AD79, the inhabitants of Pompeii on the Bay of Naples saw an astonishing sight: a column of smoke bursting into the sky from Vesuvius, the huge volcanic mountain that looms over the bay. According to an eyewitness, Pliny the Younger, writing 20 years after the event, the cloud reached nine miles in height (it resembled a fir tree, he said) and dropped burning ash upon the town.

The Pompeiians were used to natural disasters – there had been an earthquake 17 years earlier, in AD62 – but they were alarmed by the force of the ash-rain falling on their streets and houses. Many took to their heels with families and slaves, taking with them valuable jewellery, favourite pots or candlesticks, and their life savings. Some headed for the beach, thinking they might be safe in the water; others ran through the city, seeking whatever safety lay outside its gates. All afternoon and evening, they packed belongings, said goodbyes, and set off across an increasingly thick pumice carpet, in flight from the abysmal conflagration reddening the sky behind them.

At midnight, the column of fire and cloud, the vast toxic fir tree, was 19 miles high. Boiling lava poured down the mountainside. Then, at 1am on 25 August, the end came. A massive, biblical torrent poured out of Vesuvius and stamped on the town like a gigantic foot: a 900-degree super-cloud of gas, ash, molten rock and volcanic debris, travelling at astounding speed – it was later described as a "pyroclastic surge" – killed the fleeing townsfolk in their tracks. Scientists have long assumed they died of asphyxiation; in fact, they probably died of thermal shock, in a fraction of a second.

Silence fell on Pompeii and Herculaneum for 1,700 years, until the first excavations began. And what was unearthed in the next two centuries became a wonder of the world: skeletons with decayed teeth intact, buildings with their interiors, wallpaper and graffiti perfectly preserved, 81 loaves found in a bakery looking as though just extracted from a too-hot oven. When 19th-century archaeologists made plaster casts of the spaces left by the bodies, they revealed close-up details of clothing, hair, facial expressions – a population captured at the moment of their death.

And an ancient city captured in a freeze-frame? That's the unique selling point which has brought millions to walk around the partially engulfed, partially recovered Pompeii, feeling they're walking down streets unchanged in two millennia. It's the subject of a television documentary on 14 December, in which the Cambridge classics don Professor Mary Beard tries to confront several long-held myths.

A striking woman of 55 with a mane of ash-blond hair and a tendency to refer to herself in the third person, Mary Beard represents the human face of academe. She talks in slangy demotic, miles removed from high-table Oxbridge. She loves appearing in the media, dilating on classical issues on Radio 4's Start the Week, debating the merits of the 20th-century novel at the Hay Festival. Her popular blog, A Don's Life, deals with an eclectic mass of subjects, from modern America's culpability in terrorist attacks to the time she was raped on an Italian train by a man who bought her a ticket.

In the television show, she prowls the streets of Pompeii like a detective, deducing, inferring, teasing out a thousand tiny physical details about Roman life in AD79, in the streets, the baths, the shops, the homes, even the sewers of the petrified necropolis.

"Nobody in the ancient world wrote about Pompeii, before the disaster," she tells me. "Nobody famous or interesting came from there. It was so utterly ordinary, it didn't come to anyone's attention. I always hesitate to find a modern British parallel, because you're going to insult somebody's home town if you say it resembles, say, Letchworth."

She has been theorising about the place and its inhabitants for 30-odd years. "I first encountered Pompeii when I was 18, in my first year. We'd learnt about the place as a rather boring sort of Roman wall painting and I went along rather dutifully. When I got there, I thought, my God, they never told me it was like this. Of all the places in the world, it was the only one where you can step back into the ancient world. But why I've studied and taught it for nigh on 30 years is that, when it comes to understanding Pompeii, anybody can do it. As long as the questions you ask are interesting, and your brain is in gear and both eyes open, you can learn a lot."

She imagines Pompeii as a bustling, raffish town of 12,000 inhabitants, to which visitors came to gamble and have sex ("a cross between Brighton and Las Vegas"). She checks out the streets with a commonsensical eye. "Think of Up Pompeii! or movies about Rome and what do they look like? Large, white, marble, sparkling and clean. But look at the streets and you find there's no drainage. What are these stepping stones doing in the street? They're there because the streets are full of shit and water. The biggest myth we're trying to burst is that the ancient world is somehow not real. We're saying it's real and smelly and dirty and noisy."

To further her researches, Professor Beard descends into the sewer of a private house, noting the greeny-brown stains on the wall and discovering 70 bags of ancient human excrement about to be microscopically inspected at Oxford University. "I've often longed to put my hand inside a bag of ancient shit," she confides. "Eventually, I did. It was like potting compost. I thought it would be slimy and smelly – but no, rich potting compost, like the stuff you buy at the garden centre." She also reveals the slightly disgusting nature of Pompeii's popular baths, where citizens piled in together, where urine and sweat mingled with the water and there's no sign of how it drained away. "Make sure you don't go to the baths with an open wound," she counsels. "You're likely to die of gangrene if you do."

The archaeological focus of her television show is a trove, if that's the word, of 54 bodies unearthed about 10 years ago in the basement of a house in Oplontis, a suburb of Pompeii. "It was a rescue operation," Professor Beard says. "They were building a new school, and, in doing so, they came across these remains. But there's been a very limited chance of examining them until now." Many of the bodies were carrying sums of money when they fell [there were no banks in Pompeii], or gold jewellery or loose valuables. Some of the victims' bones revealed a greenish tinge, a sure sign that they'd been buried near bronze and copper objects. We can't tell, though, which of these people were rich and which were slaves carrying money for their masters."

Professor Beard is keen to explain how masters and slaves in Pompeii lived in claustrophobically close proximity – how slaves sometimes slept like dogs at the end of their masters' beds; how their masters ate, talked and sometimes fornicated in front of them, as if they weren't there.

It's hard to keep Professor Beard off the subject of Pompeii and sex, because a) it's one of her major hobby horses (many undergraduates at the Cambridge classics faculty have been startled by her introductory lecture on lewd Roman graffiti) and b) sex is everywhere in the ruined city. The Pompeiians were a bizarrely sexualised bunch. Wherever you wander, 2,000 years later, they still greet each other with genial sexual insults and gossip in surviving graffiti. Erotic paintings, obscene frescos and rude inscriptions ("Maritimus licks your vulva for 4As") are ubiquitous. Plaster phalluses and testicles point to the sky or the horizon like the stylised pointing fingers in Victorian advertisements. "We're sure that, in Pompeii, sex was available for money, just like in 21st-century London," Professor Beard says. "Some archaeologists have located 35 brothels in Pompeii, but I think I've narrowed it down to one."

How could she tell it was a brothel? Rather than a hotel?

"It's not hard to distinguish today between a hotel and a massage parlour," the professor says defensively, "when you get the combination of five cell-like rooms, the decor, which consists entirely of paintings of different positions of sexual intercourse..."

That doesn't make it a brothel, I point out. It could be an unusually liberal monastery.

"...and the graffiti," she continues, ignoring me, "97.5 per cent of which says, 'I had a great fuck here' – well, call me a fool, but I'd say the dice are stacked in favour of it having been a brothel."

And the phalluses that appear on every street corner? "If you consult the guidebooks," she says, "they'll tell you the willies point to the nearest brothel. Or they'll go into lots of pseudo-anthropology about fertility of warding off the evil eye. I want to say, what you're seeing here is a society quite different from ours. In Roman culture, however much women might get on, power and masculinity are co-related. When you find a sculpture of a willy over a bread oven, it's not to dispel the evil eye, it's simply to say, 'Look, it's me, the male baker.' I think, at some level, that's the answer."

There's something very bracing about Professor Beard's approach to archaeology, her plunge-your-hands-in-the-shit earthiness, her jolly zeal for matters of food, drunkenness, drainage, and other domestic issues (one chapter of her book starts with the arrival, on the last morning, of painters and decorators), her nailing of schoolboy mistakes ("Did I find a vomitorium? Oh come on, John, you know what a terrible myth that is. A vomitorium is the exit from a theatre, where people are vomited out into the street") and her irrepressible sauciness. It's not every day that you get a Cambridge don of the utmost moral rectitude uttering the word "cocksucker" on television, while translating an early strip-cartoon found in a Pompeii bar.

"It was, I should point out, an absolutely straight, indeed pedantic, translation from the Latin," she bridles. You feel the people of Pompeii, whose daily lives she so winningly evokes, would have welcomed her as one of their own.

'Pompeii: The Life of a Roman Town' by Mary Beard, Profile Books, £9.99.

'Pompeii: Life and Death in a Roman Town' is broadcast on BBC2 on 14 December