City of Sin: London and its vices, By Catharine Arnold

In 1180, a monk named Richard Devizes wrote of how he disliked London, a city filled with "jesters, smooth-skinned lads, Moors, flatterers, pretty boys, effeminates, pederasts, singing and dancing girls, quacks, belly-dancers, sorceresses, extortioners, night-wanderers, magicians, mimes, beggars, [and] buffoons." He concluded, "if you do not want to dwell with evil-doers, do not live in London."

But lots of people have been only too delighted to dwell with such things over the years, and City of Sin is their story. It is the third in a trilogy of lively London histories by Catharine Arnold, the others being on death and madness. In each, she leads us briskly and entertainingly through her theme – "vice" here translating mainly as "sex". To pack 2,000 years of the stuff into less than 400 pages is a challenge, but Arnold achieves it admirably.

Her narrative begins with the prostitutes imported to the city in Roman times. They were issued with licences and inspected for disease; apparently they wore leather bikinis by way of uniform. But their lot was miserable, for they were slaves, who had no choice and earned no money. It was not the last time women in London would be caught in such a trap, although Arnold points out that the "white slavery" panic of the 19th century was mostly a myth.

Abuses and servitude continue today. But most sex workers of the past seem to have found their way into the job themselves, driven by financial need or more rarely by vocation. A few have always done well out of it, retiring on their savings or becoming entrepreneurs in other fields.

Interference by municipal authorities has been a constant, beginning with Henri II's laws prescribing that brothels be run by men. The Puritan Revolution shut down theatres and disorderly houses completely. As recently as 2009, high-class escorts were evicted from their Shepherd's Market flats in Mayfair on the excuse that they were altering the use of the property – a strange argument, since such use has been traditional since the 18th century.

Between killjoy interludes, happy times were to be had. In the early 17th century, visiting Swiss physician Thomas Platter described what sound like ladettes: women who loved being plied with glasses of sugary wine in taverns – and "if one woman is invited, then she will bring three or four other women along, and they gaily toast each other".

If London was a good place to be gay in either of the old senses ("in good spirits" or "on the game"), it was also a surprisingly good place to be gay in the sense we know today. Although male homosexuality was illegal, the 18th-century city sported venues such as Mother Clap's Molly-House, where men could dress up as shepherdesses, indulge in casual sex, and have a good time. There were lesbian equivalents too: Mother Courage's in Suffolk Street, and Frances Bradshaw's in Bow Street.

The Victorian era brought darker forces into play. Philanthropists such as Josephine Butler set out to wipe prostitution off the face of the earth – futile goal – and Jack the Ripper preyed on East End streetwalkers. Only after two 20th-century wars brought floods of eager servicemen into London did attitudes relax. By the 1970s, people responded to sex scandals with amusement more than anything. The raids in 1978 on Cynthia Payne's suburban brothel, filled with eminent lawyers and vicars in bondage or wearing nappies, was greeted with nationwide tittering, and Payne's trial for running a disorderly house ended with acquittal. On the courthouse steps, she hailed this as "a victory for common sense".

City of Sin covers a range of other activities, from pornography to flagellation. Here, too, the story alternates between repression and sensible acceptance. We meet characters such as Victorian collector Henry Spencer Ashbee, who left 15,299 items of pornography to the British Museum and obliged that august institution to take them as a condition of also getting his valuable Cervantes editions, and the inventor Chace Pine, who designed an ingenuous machine that could whip forty people at once.

Arnold ends upliftingly, with Andrew Marvell's "Ode to his Coy Mistress". Marvell urges his lover to live for present pleasure, rather than clinging to virtues destined to wither and rot in the grave. "Now let us sport us while we may," he says. It is a fitting epigraph for a story in which simple human libido and exuberance keep London's streets alive.

Sarah Bakewell's life of Montaigne, 'How to Live', is published by Chatto & Windus