On 28 May 1667, Samuel Pepys took a boat along the Thames to Vauxhall, "and there walked in Spring-garden; a great deal of company, and the weather and garden pleasant". He noted that it was "cheap going thither, for a man may go to spend what he will . . . but to hear a nightingale and other birds, and here fiddles, and there a harp, and here a jews trump, and here laughing, and there fine people walking, is mighty divertising".

Vauxhall was then a rural hamlet on the south bank of the Thames, and Spring Garden  later known as Vauxhall Gardens  was "a pretty contriv'd plantation", as John Evelyn described it in 1661, a square plot fringed by trees with a house on the western side, where (to cite a Dutch visitor) "lots of people came to amuse and refresh themselves". In his Diary, Pepys describes many trips there, during which he saw acrobats do "tumbling tricks" and was "troubled" by the sight of "two pretty women" being pestered by "some idle gentlemen", sadly a common experience at the gardens throughout their history.

As David Coke and Alan Borg say, London at this time was "filthy, malodorous, violent, cacophonous and disorderly, the kind of place where an unwanted baby could be left to die on a street corner, or a bear be torn to bits by mastiffs simply for the amusement of the mob". In an age when most of the city's entertainments involved cruelty or violence, Pepys's visits to Spring Garden reveal a widespread desire for a civilised environment in which people could enjoy themselves  "a universal withdrawing-room for the city".

The pleasure garden was the result, an idea that was taken up in cities across Europe and America. A fee was charged for admittance and people were entertained, usually in the evening, with music and refreshments. Open to all who could afford the entry price, the leafy pleasure gardens were egalitarian spaces where commoners could rub shoulders with aristocrats. Vauxhall Gardens was the first and most famous. In 1729 a dynamic young entrepreneur from Bermondsey took over the lease. Jonathan Tyers wanted his pleasure garden to become (as he put it) a "rational, elegant, and innocent" space, a civilised and civilising environment.

These were lofty aims, and down-to-earth Londoners were not easily convinced. William Hogarth is said to have come across Tyers sitting dejectedly near his gardens, contemplating suicide because he feared his venture was going to be a disaster. Hogarth dissuaded him and told him he knew how to realise Tyers's vision of (what a friend later called) a "rational and elegant Entertainment". It is not known exactly what Hogarth said, but clearly Tyers valued his advice: he presented Hogarth with a golden lifetime pass to the gardens as a token of his gratitude.

With Hogarth's help, Tyers transformed what was essentially a plantation of trees into a space for performance and display, with specially designed pavilions, grottoes, sculptures and illuminated serpentine walks. The Orchestra, an octagonal building designed for the performance of music in the open air, was opened in 1735, the first of its kind in England. Around it in colonnades, he built rows of supper-boxes where people could enjoy the music while eating and drinking. The central grove, with its classical portico at one end, was like "an ancient Greek agora". It could accommodate 3,000 people. With 100,000 visitors each season, the gardens provided London-based composers with their first mass audiences.

As this meticulously researched and very readable history shows, Tyers was hugely influential as a patron and promoter. Through his choice of architecture, paintings, sculpture, furniture, tableware, lighting and, of course, music, Vauxhall Gardens became "the nursery of the British rococo style".

It must have been a truly magical experience to wander through the gardens at night, along tree-lined gravel walks, with bird-song and music in the air and light from the 20,000 oil-lamps twinkling among the branches (William Wordsworth, who visited aged 18, was struck by the "wilderness of lamps / Dimming the stars"). For 18th-century Londoners, it must have seemed like stepping into a dream world. As Fanny Burney's heroine Evelina says, it was "enchanted ground". Tyers was constantly trying to enhance the ethereal atmosphere. He even experimented with what were known as "Musical Bushes". An underground chamber was excavated close to a statue of Milton in which the poor musicians had to play, creating the effect of disembodied music, or as it was then described, "subterraneous musical sounds . . . called by some the fairy music".

Music, wine and moonlight: it was a recipe for romance. John Keats penned a sonnet in 1818 "To a Lady seen for a few Moments at Vauxhall". As a setting for romantic intrigue and sexual danger, writers and novelists, such as Tyers's friend Henry Fielding, Tobias Smollett, Thackeray and Oliver Goldsmith, found it irresistible. From Pepys's day until its final season in 1859, there were continual complaints about "loose women" and the unwanted attentions of "Bucks". In 1712, Joseph Addison reported how a friend wished "there were more Nightingales, and fewer Strumpets". Magistrates later forced Tyers to provide lighting in Lovers' Walk to discourage "immoral behaviour". But, as the authors say, "the al fresco character of Vauxhall and its intimations of physical and moral danger were essential features of its popular appeal".

The heyday of the gardens was during Tyers's period of ownership. They were open for 70 years before he took them on and for 80 years after he died in 1767, but it was his vision and idealism that made the word Vauxhall synonymous around the world with pleasure gardens. Under his proprietorship  and he was a hands-on manager, even serving behind the bar  it became an idyllic refuge from the noise and filth of London's streets and the "most successful commercial public attraction of the Georgian period". Sadly, nothing now remains at Vauxhall of the gardens, just "an open green space fringed by inelegant tower blocks". But Coke and Borg have tracked down a rich trove of artefacts, ranging from paintings to silver season tickets, many of which are illustrated in this beautifully produced biography of what was once one of London's best-loved institutions.

PD Smith's history of cities will be published by Bloomsbury in March 2012.

If you go to the site of Vauxhall Gardens now, you will find a ragged patch of grass near to a demonic concatenation of bad architecture and violent traffic engineering. All trace of the gardens' purpose  pleasure  has vanished. Mentioned in Pepys, Fielding, Keats and Thackeray, and many other writers, the gardens now seem a myth, a figment, little more than an evocative name for something that seemingly was never there.

Yet the gardens very much were there, remarkably, from 1661 to 1859: how many other places of entertainment, subject to fluctuations in taste and fragile finances, last two centuries? Its success was despite the fact that this open-air place was exposed to the weather, and for most of its life was reached by a precarious boat ride from central London. And despite, too, the legendary expense of its food and the money-saving, extra-thin slicing of its meat. It even survived the attempt of Jonathan Tyers, its forceful proprietor from 1729 to 1767, to make it a place of morally improving entertainment, which might be thought a suicidal business proposition.

David Coke and Alan Borg have written a weighty, scholarly book that gives substance and detail to this chimera. If feels as if every possible detail and document relating to the gardens have been scanned and assimilated. The result is the most complete reconstruction of this vital place there is likely to be.

What emerges is an alter ego of London, essential to the city but apart from it, a magical-tawdry place of appearances, shadows, sensuality, transience, tolerance and other things suppressed by the hard forms of the city proper. Historically, it stood between the aristocratic gardens of the European Renaissance, and the music hall and the seaside pier of Victorian mass entertainment, between Tivoli and Blackpool. It offered dining and drinking, music, art and, increasingly as it struggled to fight off competitors near the end of its life, acrobatics, fireworks, wild animals and balloon flights.

It was a social mixer, patronised by the Prince of Wales and aristocrats, but also by writers, artists and ordinary people. One of Tyers's more idealistic aims was to make a place of freedom, a prototype for a more egalitarian future. He also achieved a fusion of high and low art: music by Handel, paintings by Hogarth and Francis Hayman, mixed up with the spirit of the fairground. Music was not heard, as in a concert hall, in silent rows facing the players. It permeated the gardens, forming a background to everything else that was going on.

When the gardens are remembered now, it is often as a place of sex, paid for and otherwise. And so it was, especially in the first decades before Tyers took it on. His campaign of moral improvement did not  unsurprisingly  make the gardens chaste, but it made the prostitution and assignations less blatant, just enough to make it respectable for royalty and families to visit. His gestures of propriety were not so dumb after all  they allowed the gardens' attractions to take many forms.

Fashions could be displayed, patriotic triumphs celebrated, and great music performed at the same time that shady walks and shrubberies allowed ample scope for shagging, or for the Victorian man who delighted in hiding in the bushes so he could hear "hundreds" of women urinating. Possibly, the gardens were no more Bacchanalian than central London: according to Dan Cruickshank's Secret History of Georgian London, most of Fleet Street, the Strand, Covent Garden and St James's Park was in effect an open-air brothel. One secret of the gardens seems to have been their relative subtlety, their tempering of function with fantasy.

The design of the gardens was simple: a rectangle divided by a grid of avenues and paths, with light, playful pavilions in classical, gothic and Chinese styles. There was interplay between the built and the planted, and structures and trees combined to make the spaces needed for the gardens' pleasures. Near the entrance sinuous colonnades contained supper boxes, which like theatre boxes were places for seeing from and being seen. In the centre was a pavilion for musicians. The essential architectural element was light, with artificial lamps to prolong the enjoyment of food and music, and increase the management's financial take, and the equally necessary darkness of the shady walks.

Tyers was a sort of entrepreneurial Prospero, and under his and his heirs' management the gardens had their best decades. The authors of the book are uncertain why they finally declined and fell. Bad weather was blamed at the time, but as the gardens had been there since the 17th century, this is hardly convincing. Coke and Borg cite the growth of the city, which made the gardens less of a rural idyll, and the rise of rival attractions, such as early music halls, and the Crystal Palace, which was relocated to Sydenham from Hyde Park in 1854. There was also more money to be made by building houses on the site (whose streets, after bombing in the second world war, would return to grass). Surprisingly, the authors do not dwell on one reason sometimes given for the gardens' decline, which is that railways made it easy to reach more distant attractions, such as the seaside.

With their methodical style, Coke and Borg do not quite conjure the gaiety of their subject. But at the end of the book are published the only two known photographs of the gardens. They catch your breath. Here is a creation from the age of Samuel Pepys, a thing of legend, captured with a camera. It is like seeing a photograph of a unicorn, or a dodo, or Atlantis.