The opening bars of Ralph Vaughan Williams’s A London Symphony (1914) are scooped out from the gloopy bedrock of the city. Vaughan Williams was dredging through the same mud, silt, slime and ooze as those scene-setting paragraphs of Our Mutual Friend (1865), where Charles Dickens shows that the real glue binding his book together will be the River Thames.

Dickens’s famed ‘boat of dirty and disreputable appearance’ berths Our Mutual Friend in the earth and experience of London. Similarly, Vaughan Williams’s cellos and double basses, which launch his symphony, plod out from the sludge of the river. But, by the time his bucolic Scherzo waddles into view, you could be forgiven for assuming that RVW has taken a genteel amble around the countryside. Little about his sepia mood-music suggests a city on the cusp of the modern age.

Dickens becomes the seedbed of a whole tradition of London literature, from Arthur Conan Doyle to Will Self, Patrick Hamilton to Martin Amis. And what did Vaughan Williams’s symphony spawn? Precisely nothing. The project of making a classical music of, and about, London was unceremoniously dropped in a ditch.

Could tapping into an inherent sound of London even be possible? That question has wormed its way through my brain for years, and two newly published books have brought it back to the surface. Iain Sinclair’s London Overground: a Day’s Walk Around the Ginger Line takes an orbital journey around the city. The newly completed London Overground circuit allows the pyschogeographically minded author to take a fresh measure of the city. Sinclair tags the terrain by writer. Battersea was Angela Carter’s patch; Camden connects to one-time resident Arthur Rimbaud; Chelsea’s new-build Millennium Harbour feels like a J.G. Ballard dystopia waiting to happen. As a music-writer and lover of London myself, I feel a degree of envy. Why does plotting an equivalent sound map of the city feel like such an impossible dream? Where exactly is London’s music?

In his Words Without Music — a Memoir, Philip Glass straightforwardly states that his music ‘sounds like New York City’. And whether it’s the early-period minimalism of Glass, the bebop of Charlie Parker, the modernist complexity of Elliott Carter, the Studio 54 disco of Chic or the CBGBs punk of The Ramones, the base sound of New York’s high-velocity music is etched and scored over the city grid; the tension of line running against line. The hectic silence of John Cage is an upended acknowledgment of the same phenomenon.

But — ‘my music sounds like London’? That would be a grand assertion indeed, and unsurprisingly, no one has tried to claim the identity of ‘London composer’. The problems are practical, political and aesthetic. A river might run through it, but not enough to unify the geographical immensity of the urban sprawl: Barnet in the far north, Crystal Palace spilling into Croydon in the deep south. ‘Composing a valid structure that took in the entirety of London,’ Sinclair tells me, ‘would be a massive, intense undertaking. Writers regularly draw on all kinds of literary genealogy. Walking down the Old Kent Road to Canterbury you think of Chaucer — then retellings by Blake and Pasolini. But I’m not certain how you would approach that same project in sound.’

Light-music follies by the likes of Eric Coates approached a representation of London in sound as a sequence of picture postcards. When the French composer Edgard Varèse pitched up in Manhattan in 1915 he was immediately inspired by the city’s New World itch. His orchestral masterwork Amériques blasted harmony, rhythm and orchestration into the realm of science fiction — only seven years after RVW’s decidedly earthbound symphony.

British composers, though, especially the eagle-eared generation of Harrison Birtwistle and Peter Maxwell Davies (both born 1934) and Cornelius Cardew (born 1936) would hit an aesthetic wall. The legacy of Elgar and his contemporaries had the stench of Edwardiana and colonialism. For composers weaning themselves on Webern, Stockhausen and Cage, London was a living symbol of old-school starch, its grand architecture and gesturing statues an absolute aesthetic mismatch. London was a place where music publishers had offices and premières happened. Then you got out. Cardew relocated to Cologne; Birtwistle to rural France; Maxwell Davies to remotest Orkney. American composers were sucked willingly inside the New York experience, while London repelled their British counterparts.

But London was a place where music happened. In the late 1950s, Soho was oxygenated by sound. At the top of Old Compton Street, near the junction with Wardour Street, the 2i’s Coffee Shop provided a platform — actually more a tiny raised stage — for emerging popsters such as Cliff Richard, Tommy Steele and Adam Faith. On Wardour Street itself, the Marquee Club ran a programme of blues and rock. Walk the opposite way out of Old Compton Street and you’d enter the realm of a club founded by the trad jazz clarinettist Cy Laurie.

Meanwhile, in Muswell Hill in the north of the city, brothers Ray and Dave Davies were busy overhauling their rough-and-ready childhood band The Ravens to form The Kinks — a group that dealt with the American mother music in a noticeably different way from The Rolling Stones, who operated out of Chelsea in west London from where, a decade later, the Sex Pistols would shock and maim polite sensibilities. And some of this music begins to resonate in the imagination as a London music. Ray Davies’s ‘Waterloo Sunset’ floats our ears back along the dirty old river, the Thames flowing metaphorically through a love song; and the two-fingered salute of punk, while it lasted, was locally incubated rage.

Detach the music’s profound social consequences from the notes and structures, however, and the apparent triumph of jazz, pop and rock musicians — succeeding in establishing local music scenes where classical composers had bottled it — comes with qualifications. I’m Kinks-fixated, and the hellish roar of ‘London’s Burning’ by The Clash unfailingly ignites my soul. But in New York, engagement with the magnitude of the city obliged musical form to bend, buckle, extend, fuse and generally renew. Glass moulds the base molecules of tonality into open-ended mantras; the late Ornette Coleman scatters the component parts of blues and bebop into an abstract free-form jazz funk. London proves itself more adept at hosting home-made versions of imported musical styles: jazz, blues and rock spoken with an accent.

With one major exception. Beginning in 1966, a pool of musicians well versed in jazz that took an interest in notated modern composition gathered in the Little Theatre Club, housed in a nondescript courtyard in Covent Garden. Saxophonist Evan Parker, guitarist Derek Bailey, drummer John Stevens and trombonist Paul Rutherford respected jazz tradition too deeply merely to impersonate. Instead they deconstructed the accepted vocabulary of music and instrumental technique. Free improvisation riffed off the cultural disorientation and scale of the city, a uniquely authentic London solution to the problem of what to play.

In Dickens’s day, the river and the tolling of church bells dominated the soundscape; today what Iain Sinclair calls the ‘orgasmic sighs and moans’ of the London Overground has become another layer inside a complex urban fugue of blaring traffic, honking sirens and smartphone chatter. But if places really can form imaginations, the London Overground has rewritten the shape of the city in a way that makes the prospect of finding any concrete answers to that key question — where is London’s music? — increasingly unlikely. ‘The need people had,’ Sinclair says, ‘to make a physical journey from the suburbs into, for instance, Soho because they were into this particular kind of music, these clothes or books — travelling between constricted suburbia and these apparent freedoms at the centre — those journeys of inward motion no longer exist. Now everything is connected with everything else; every place is like another.’