Most Londoners could name only the river, but dozens of waterways used to feed the Thames. Centuries of building and paving has consigned many, including the Fleet, the Effra, and the Tyburn, to the city's bowels. Others, including the Walbrook, which once bubbled and flowed through the oldest part of the capital, are no more than dry voids.
The classic book on this topic is The Lost Rivers of London (Nicholas Barton, Historical Publications, 1992, ISBN-10: 094866715X): this is a revised edition from the original The Lost Rivers of London; a Study of Their Effects Upon London and Londoners and the Effects of London and Londoners Upon Them, a surprise hit of 1962 based on Barton's PhD thesis. We had a copy a while back, and I found it gripping, perhaps because of its combination of informative research about a (then) little-known aspect of London's origins and the strong air of nostalgia surrounding the topic (though the reality is that these rivers, by the time they were covered up, were ghastly open sewers). I wrote about this when JSBlog had just started up - see Underground London - but I'll repost for convenience.
There's a nice map at The Open Guide to London Lost Rivers page, and a good overview at Barryoneoff's Rivers that disappeared. This defunct Heritage Magazine article, The Underground City, with topological map, gives more context on how the main rivers interact with other features. London Geezer's series of blog posts, Reviewing the Fleet is a superb study of the complex history of the River Fleet (now a sewer / storm drain).
However, an interesting development since then has been the plan to restore many of these lost waterways - see Lost rivers of London to resurface in Boris plan (Danny Brierley, Evening Standard, 16 June 2008) and River rescue: project launched to breathe life into waterways buried under London concrete and brick (Juliette Jowit, The Guardian, 8 January 2009). Some of the ideas are bold and intriguing, such as the one to change Fleet Street, originally the course of the Fleet, into a Venetian-style waterway. This isn't a new-fangled concept; it was actually done as part of Sir Christopher Wren's redevelopment of London after the Great Fire. Wren converted the lower reaches of the Fleet (bordered by slums before the Fire) into the New Canal, with four decorative bridges. The canal basin's lack of commercial success, tendency to silt up, and the increasingly disgusting state of the Fleet ...
Now from all Parts the swelling Kennels flow,
And bear their Trophies with them as they go:
Filth of all Hues and Odours seem to tell
What Streets they sail'd from, by the Sight and Smell.
They, as each Torrent drives, with rapid Force
From Smithfield, or St.Pulchre's shape their Course,
And in huge Confluent join at Snow-Hill Ridge,
Fall from the Conduit prone to Holborn-Bridge.
Sweepings from Butchers Stalls, Dung, Guts, and Blood,
Drown'd Puppies, stinking Sprats, all drench'd in Mud,
Dead Cats and Turnips-Tops come tumbling down the Flood.
- Jonathan Swift, Description of a City Shower, 1710
To where Fleet ditch, with disemboguing streams
Rolls the large tribute of dead dogs to the Thames
- Alexander Pope, Dunciad, 1729
... led to the New Canal being filled in and paved over in the 1730s. The Fleet's course is now well known; the Environment Agency, however, is pessimistic about it being restorable to surface view.
By the way, the Guardian piece about Walbrook mentions Ursula Fanthorpe's poem on the lost rivers of London, "Rising Damp": it featured as the Independent's Sunday poem for 20th June 1999.
While London is particularly iconic with respect to its vanished watercourses, the same picture applies to just about any major city. See, for instance, Lost River Walks and Construction will need to protect lost rivers concerning Toronto, whose underground legacy is the result of the original creek and ridge terrain; Montreal is similar, likewise Manhattan (as revealed by the Viele Map) and Los Angeles. Paris has the Bièvre and the Ruisseau de Ménilmontant; but as Céline Knidler's Sorbonne thesis Le Paris souterrain dans la littérature says, the Grange-Batelière appears to be mythical, though this story of a navigable underground river was part of the inspiration for The Phantom of the Opera. (Paris, of course, has its own vast underworld in the form of its famous Catacombs, tunnels of abandoned mines for gypsum - whence Plaster of Paris - and building stone).
Closer to home, a couple of pertinent books spring to mind: Secret Underground Bristol (Sally Watson, Broadcast Books, 2002, ISBN: 1 874092 95 8) and The Lost City of Exeter (Chips Barber, Obelisk Publications, 1982, ISBN 0 946651). The Watson book explores a city with a remarkably complex underlife resulting from its geology (cave-ridden limestone, red Triassic sandstone and Coal Measures): topics include Goldney and Warmley grottoes, Bristol coal mines, caves such as Pen Park Hole, Redcliffe Caves and Giant's Cave, sewers and drains, the Hotwells hot springs, the Clifton Rocks Railway, the River Frome, and mediaeval cellars and conduits (such as St John's Conduit and Temple Pipe).
Though we do have underground passages (a mediaeval water conduit), underground Exeter is rather less complicated. Nevertheless, The Lost City of Exeter has a chapter on The Lost Streams of Exeter; I didn't realise until recently that the broad cutting at Exeter Central Station, between Rougemont Castle and the prison, actually follows the natural Longbrook Valley, whose stream flowed to the Exe under the Iron Bridge. Another stream began near what's now Chute Street (tagged in the map below) and ran SSW along what's now Western Way.
It was called the Barnfield Brook, but its older name, the Shit Brook, indicated its use (as a fast-flowing stream emptying in the Exe downstream of the city) as a sewage conduit. (Paris Street, adjacent to Exeter Bus Station, was historically called Shitbrook Street). The stream itself went underground, as Barnfield Brook Sewer, following a cholera outbreak in 1832. It's commemorated in "The Chamber Atlas" ("in memory of John Richards of Exeter, surveyor, 1689-1778"), the first poem in James Turner's 2002 anthology Forgeries.