The mooring with the most

And then there is the location: thanks to the Yamaha 100 Ribeye 550 speedboat moored along the shore-side deck, you can be in Canary Wharf in 15 minutes, Westminster in only five and Chelsea in 10. "Although my record was eight when I was very late for a meeting," adds India. Could there be a better way of getting around London? All you have to do is make sure there is somewhere to moor the Rib when you get there.

The Harpy was built in 1904 by Messrs Edwards of Millwall for what was then the considerable sum of £5,211 12s 3d and positioned off Custom House Quay, a few hundred yards west of its current location. A staff of more than 75 customs men, squeezed in side by side in conditions likened by one officer to a "Chinese brothel", collected dues from the ships docked in the Pool of London, the name given to the busy stretch of river between Rotherhithe and London Bridge.

By the early 1970s most of the ships had long since gone and The Harpy, surplus to requirements, was towed to Greenwich, where it was left to rot. It was there that it was spotted by India's father, Andrew Wadsworth, who was just setting out on what was to prove a highly successful career as a property developer.

One of the first to realise the enormous potential of London's Docklands, Andrew in 1980 bought New Concordia Wharf, an abandoned 19th-century warehouse just east of Tower Bridge, which he turned into a mixture of flats and studio workshops that became a model for the other developments that quickly followed further to the east. The Harpy seemed the perfect site office, so he bought it, did it up and moored it in its current location beside the wharf.

And there it stayed as he completed this and then several other projects along the river. Then, five years ago, Andrew, who has since moved to Dorset, transformed the Harpy again, this time into its current form as a luxury pied à terre (or should that be pied à l'eau?) in the capital for the family - including India, who was about to embark on a gap year in London before starting at LSE. "I lived in halls for the first term, but was paying an extortionate rent for a box. I decided that if we had this place, then I might as well enjoy it, free of rent," she says.

The result is an idiosyncratic bright-blue-painted home, offering 1,868 sq ft of living space and a further 2,000 sq ft of terraces. The views, from both inside and out, are spectacular: The Harpy is considerably higher than most houseboats on the Thames and, thanks to its long access gangway, also further out in the water.

Spanning the entire upper deck is a 53ft-long open-plan living-eating-working area with a fully equipped kitchen at one end, dining table in the middle and reception area at the other. The furnishings are an eclectic mixture of period pieces dating back to the 1920s, collected by Andrew. Hanging from the ceiling is a model of a 1940s US Corsair fighter plane, which sways with the motion of the pontoon. On the level below are a master bedroom and en-suite bathroom with cast-iron bath and separate shower, as well as three further bedrooms, a guest bathroom and guest cloakroom.

Some of the paintings on the walls are by Andrew's wife, Julie, who studied with Damien Hirst and the other Young British Artists at Goldsmiths college. Photographs on a sideboard show Andrew variously with Ronald Reagan, Prince Charles and John Major.

You may not be on dry land, but that doesn't mean you have to give up on creature comforts such as mains gas, water and electricity and gas-fired central heating. The floors are solid oak, and the windows on the upper deck are restored original Edwardian sashes. And there are all the techie gadgets: landlines in every room, of course, as well as Wi-Fi, a 48in TV with surround sound and a seven-speaker Bose music system.

With India off to New York to pursue the career in acting and modelling, and neither her younger brother, Hugo, 21, nor her sister, Rosannah, 18, in London, The Harpy is - for the time being - surplus to requirements. The Wadsworths are understandably reluctant to part with it, though, and so are letting it out rather than selling it.

"After this was no longer needed as an office in London and there were some hint of selling it, both my mother and I were in tears, saying, 'You can't do it,'" India says.

Andrew, at present involved with a large-scale development project in the centre of Dorchester, hasn't been short of offers for The Harpy. Richard Branson expressed an interest in buying it a decade ago, as did the film director Rocky Morton, who was responsible for Super Mario Bros. Andrew refused both, although he did allow Morton to stay for a week on the pontoon.

The Harpy will most likely appeal to a well-heeled "creative" looking for a live/work unit with some of best outside entertaining space in London - although probably without young children. As a sweetener, the Wadsworths are throwing in four spaces in the car park on nearby Mill Street and access to the pool in New Concordia Wharf. Oh, and use of the Rib.

At £3,500 a week it is not cheap, especially as, for the same budget, you could rent one of the best penthouses on the river - and still have money left over to buy a speedboat of your own.

For Simon Harris, managing director of the letting agents Unique Property Company, the price tag reflects The Harpy's novelty value . "I've been in lots of fantastic penthouses, but they don't feel like this," he says. "Often, you're sitting in the living room and you don't even see the river. There are houseboats and there are houses on the river, but this is almost like a freehold detached floating house. It's a complete one-off."

Which only leaves the constant swaying and disconcerting thumps. "Stay here for a day and you get really used to it," says India. "It's wonderful when you lie in the bath or when it rocks you to sleep. It's only when you step onto land that it feels strange."

The Harpy is for rent for £3,500 a week through Unique Property Company; 0870 900 4050, uniquepropertycompany.co.uk

No mucking about with these boats (Emma Wells)

If you've always lusted after a floating home of your own, these two seaworthy vessels need new skippers.

Solace is a newly built, 3,455 sq ft houseboat, with four double bedrooms, a 30ft reception room and a 68ft roof terrace, plus two further terraces. With three staircases and a docking platform, Solace, moored at Eastfields Avenue, SW18, part of Wandsworth's Riverside Quarter, has access to a swimming pool and gym. It also comes with parking for one car. The service charge is £4,000 per annum. It is for sale for £1.3m with Winkworth (020 8788 9295, winkworth.co.uk).

For something more classic to pootle about on, Nostalgia X is a 1950s steel motor cruiser, with a mahogany interior and plenty of glamorous associations - it was once used by Frank Sinatra to entertain the stars of his day in the Med.

Moored in St Katharine Docks, in east London (at a cost of about £1,000 a month), it has three double bedrooms, each with their own bathroom, a dining room that seats eight and a spacious saloon. The price of the cruiser - which could be rented out for corporate events, parties and holiday charters - was recently reduced from £750,000 to £550,000, as it needs some TLC.

Despite its old-world charm, and a top speed of 15mph, the boat has modern navigation equipment. So make like Ol' Blue Eyes, crank up the gramophone, get your steward to mix some gimlets - and you're off (Edwin de Lisle; 01536 770585).