This may not seem a glaring cultural omission, given that Soho and its diverse subcultures have traditionally proved as compelling a tourist attraction as any of the better-known European sex museums, most of which originated as offshoots of the adult entertainment industry.
But times are changing. Sex is moving up the cultural agenda. New institutions are being founded, while traditional museums are reassessing their approaches to sexual themes in the light of changing public attitudes.
Last month, Museums Journal learned that an organisation called the Muse Corporation is to open the London Academy of Sex and Relationships in London later this year. The fact that the curiously named venture is to be located in the London Trocadero on Piccadilly Circus has fuelled speculation as to the direction it might take.
Will it emerge as another tawdry tits-and-tableaux affair on the Amsterdam model? Or will it be more like New York's critically acclaimed Museum of Sex (MoSex) - founded by former software entrepreneur Daniel Gluck as a serious attempt 'to preserve and present the history, evolution, and cultural significance of human sexuality'?
'Titillation is not the goal,' says a spokesman for the Muse Corporation, which has hired health writer Sarah Brewer as its director of exhibits. She says the management is committed to avoiding the sleazy image that the sex industry usually conjures and has declined all funding from anyone involved in this sector.
According to Brewer, the academy will combine high tech and interactive exhibits together with new media displays, art and historic ephemera to convey health and educational messages in a fun and entertaining way.
Time will tell whether the Trocadero Academy delivers on its promise, but other recently opened sex museums in Shanghai (2000), New York (2002), and St Petersburg (2004) would seem to reflect a growing public interest in such ventures. But the commercial success of these enterprises is by no means guaranteed.
The Shanghai Sex Museum, founded by septuagenarian Chinese sexologist Liu Dalin as a showcase for his own 1,000-piece collection of vintage Chinese erotica, closed just 18 months after opening in 2000, reportedly because of low visitor numbers.
New York's MoSex was conceived by Gluck as a proper, grown-up museum devoted to the social history of sexuality in all its physical and emotional diversity.
The aim is to approach the subject through an elegant mix of levity and intellectual rigour, using cutting-edge design and compelling content to deliver a changing programme of challenging and informative exhibitions.
MoSex failed to hit its first-year target of 100,000 visitors, but, according to Gluck, things have been improving. 'We are already 50 per cent up on last year's numbers, and hope to break through 100,000, maybe to 120,000 visitors this year.
Amsterdam gets around 500,000 visitors a year and realistically we ought to be able to get 300,000-400,000 per year in New York. We're now part of the cultural discourse of the city and have been ever since we started.'
Amsterdam and New York currently represent polarised museum approaches to sex, with compromised mannequins at one end, and intellectual high seriousness at the other. Taking the serious social history path does not guarantee universal public acceptance, however, at least not in New York.
Gluck envisaged his enterprise as 'the Smithsonian of Sex,' but not everyone was convinced. 'The New York State Board of Governors wouldn't honour our name as a museum despite the list of eminent people on our advisory board,' says Gluck. 'So we decided to form it as a private venture. We're not following the existing models; we're proposing a new one.'
He expects MoSex to be profitable five years after opening, but adds that if it takes seven years, that is fine too.
Unafraid of controversy - indeed keenly aware of its PR benefits - Gluck is busy planning future exhibitions based around the risqué themes of sex and childhood and sex and religion.
Judging from the vitriolic opening volleys launched at him by the Catholic League for Religious and Civil Rights - 'MoSmut' was how Catholic League president William Donohue described the New York venture - Gluck can expect more brickbats.
'Sure, these shows will be controversial,' he says, 'but we're doing them very thoughtfully and seriously and with proper consultation with recognised authorities and experts in these fields.'
Gluck believes MoSex offers a balance to the more sanitised histories delivered by established institutions. 'I don't think other museums are taking the time to invest in these areas,' he says. 'The Museum of Modern Art's exhibition, High and Low: Modern Art and Popular Culture [1990-91], didn't address pornography as part of popular culture.
'It's totally absurd to pretend that pornography is not part of popular culture. We represent a corrective to those omissions. They have family boards and political sensitivities, but we can move more freely.'
London design agency Casson Mann has been involved in the MoSex project from the outset, designing most of its temporary exhibitions, including the 1,400 sq-metre inaugural installation, 'NYC Sex: How New York Transformed Sex in America'.
Despite the minuscule budget and the faltering start, (the museum opened just a year after 9/11), Casson Mann director Roger Mann believes Gluck's venture will eventually succeed.
'We were cautious about it at the beginning because we have a reputation for doing intelligent museums and galleries and we didn't want to ruin it by doing something cheesy or tacky,' he says. 'We were very interested early on in how "intellectual", for want of a better word, Daniel's approach to the subject was going to be.
Right from the start he was distancing himself from all the known Amsterdam and Barcelona ventures. He wants to be highly regarded as an intellectual organisation that is tackling a tricky subject, but doing it properly and in depth and being very object-rich - a proper museum really.'
Aware that his location between the Empire State and Flatiron buildings is not the most advantageous site for a museum trying to make it in New York's competitive cultural climate, Gluck is now looking for a new venue.
He is also exploring the possibility of similar satellite ventures abroad. Might these include London? All Gluck will say at this point is: 'We're talking to a very well-established person who wants to take us somewhere important.'
Roger Mann believes that if done properly, a London sex museum could work. 'Get the right combination of location, vision, and content and I think it would be brilliant. I actually think we're probably less prudish than New Yorkers in a funny kind of way.'
Whether London eventually gets its own serious sex museum or not, one thing is clear - sex is now a hot topic.
Mark Liddiard, a senior lecturer in social policy at the University of Kent, believes that sexuality has until recently been largely ignored by museums, but the focus is shifting.
'Increasingly, museums are including sexual themes in their exhibitions and programming,' says Liddiard. 'Television has been very instrumental in setting the agenda here. Museums will be seeking to address the interests of their core communities, which often include sexual and gender-related issues.'
One of the most significant of recent developments was the announcement in June this year that a new museum celebrating the history of lesbian and gay culture is planned for London. The new venture, still in the planning stage, will be run by the Proud Heritage Trust, and will seek partnerships with existing institutions in the sector.
Likely partners include the Museum of London, which has already explored sexuality in past displays, perhaps most notably in its 1999 Pride and Prejudice exhibition, a groundbreaking historical overview of homosexuality.
Darryl McIntyre, the group director of public programmes at the Museum of London, says that in future the museum will seek to treat sex as part of the dynamics of life in the city.
'We're interested in sexuality in the context of the city. Through issues of sexuality, broader cultural values get expressed. London's demographic profile is changing rapidly and we need to reflect that diversity.'
Responding to the demands of a diverse community of visitors is also an ongoing concern to London's Science Museum, which recently spun off its blockbuster exhibitions business into a new venture called Science and Media LLP.
The new enterprise aims to develop major exhibitions that will start at the Science Museum before touring internationally. Sara Milne, formerly in charge of the commercial exhibitions department, is the head of the new venture. Among her new projects is a series of exhibitions branded as The Science Of...
'The remit will be to bring the Science Museum's communications techniques to a broader audience in a way that is entertaining without undervaluing the educational aspect,' says Milne. The first of these is devoted to the Science of Aliens, but among projects still in the planning stage is the Science of Sex.
'We've been thinking about sex for a long time as a theme for an exhibition,' says Milne. 'We have all kinds of means of testing ideas - surveys, staff, schools responses, etc. Sex always appears in the top ten ideas in straw polls, but the question is how do you go about it?'
Milne says sex is a subject with many possible approaches: 'One could take a public health approach, or deal historically with changing attitudes to sex, or we could push the envelope. Should it be something that will appeal to all the family, or targeted and segmented for a more defined audience?'
How museums respond to such questions will depend to some extent on the material culture at their disposal. Many of the UK's established national museums, libraries and university collections own, or have access to, holdings of erotic or sexually orientated objects and artefacts.
The Science Museum can avail itself of the Wellcome Trust Collection, which has a wealth of intriguing material relating to sex and sexuality.
The British Museum has spread much of its erotic material throughout its collections - including the 434 items from the so-called Secretum bequeathed by George Witt in 1865, and the famous Warren Cup decorated with homoerotic scenes, formerly in the collection of the Lewes-based American collector of antiquities Edward Perry Warren.
Placing objects in the context of the culture from which they originated reveals the designs as part of everyday life, thereby annulling the synthetic frisson generated by touristic sex museums.
The financially-challenged MoSex (which has about 100,000 items of its own), is compensating for its relatively limited object collections by using software and other creative technologies to communicate its exhibition themes. But budgetary constraints can have an impact on the viewer experience.
Tim Molloy, the head of design at London's Science Museum, says: 'MoSex combined a feeling of being in a seedy porn cinema with being in a museum. But it was good to be given permission to stare and ponder things you'd normally be bashful about.
'There was a slight sense of tawdriness because of the lack of funds. You need a certain level of funding to make it feel serious. Nevertheless, it was very powerful.'
As Woody Allen once commented: 'Is sex dirty? Only when it's done right.'
Tom Flynn is a writer and journalist