What the poet didn't say was that stretches of the walk have to be conducted along what is not so much a path, more an obstacle course.
The Thames Path is one of Britain's classic long-distance trails, taking in the Chilterns, Oxford, Windsor and some of London's great riverside sights, including the Houses of Parliament and the Globe Theatre. At its best it is magnificent, at its worst, as it passes through central and east London, it becomes a nightmare. Or, as Mr Motion dubbed it last night, a monument to "Mrs Thatcher's Britain" - a reference to the luxury flats and padlocked gates that block the walker's access to the river.
The 180-mile path, which was officially opened in 1996, starts from the source of the Thames in Gloucestershire and ends at the Thames Barrier in Woolwich. The route, based on the Thames towpath and the only national trail that follows a river, was suggested as long ago as the 1930s. Proposals pushed forward by the River Thames Society and the Ramblers' Association declared the route a national trail in 1989. The Poet Laureate has found that farmers, London property developers and Railtrack have combined to make the path as challenging as the boggiest stretches of the Pennine Way - without the benefit of any fresh air.
Mr Motion has walked most of the Thames Path. Much of it is delightful, he says, but he has singled out the final leg, east of Tower Bridge, as not in the least bit pleasurable. "There's been so much building going on that you spend an amazing amount of time tracking around building sites," said Mr Motion. "I took my son along there and he got cheesed off because he thought he was going to get a riverside experience but ended up getting a tour of Mrs Thatcher's Britain. Perhaps when it's all completed there will be more walkways. It's our river after all."
Just 15 minutes' walk from HMS Belfast, close by Tower Bridge, the walker is confronted with barbed wire and concrete walls. In Bermondsey and Rotherhithe, where new developments often push strollers 100 metres inland, street names written in paint fight for space with graffiti on bare, cracked walls.
But the public is fighting back. In Greenwich, the local council will serve papers in the High Court later this month against the developers Quintains to force them to recognise the existence of a public footpath along the peninsula around the Millennium Dome in south-east London."The river is important to us and to have parts of it blocked off seems very strange," said a spokeswoman for the London Borough of Greenwich.
A little further upstream, parts of the Canary Wharf development have closed the Thames Path to walkers for the past 18 months around Westferry, while across the Isle of Dogs, the walker will come up against plush new developments with residents-only access.
Such obstructions are not new to the country's greatest river. Obstacles have been placed in front of would-be walkers on the riverside path since the 17th century, when riverside gentry blocked the efforts of Thames Commissioners trying to develop trade along the river. Today, waymarking is erratic and occasionally misleading: for a path that is supposed to follow a waterway it is surprisingly easy to get lost.
The situation is little better upstream. In Wiltshire, the local authority in Swindon has taken out path creation orders to force five landowners to allow access to the riverside near Castle Eaton. Elsewhere, Railtrack has objected to access through the viaduct at Moulsford in Oxfordshire, near Goring, and the way is also blocked around Shiplake, near Reading.
For security reasons the path does not go through the grounds of Windsor castle, but follows the north bank through Datchet vilage with a stretch along a busy public road. The Ramblers' Association had campaigned strongly for the path to through the royal estate, but the Crown Commissioners have refused access.
Residential riverside development created opportunities to reinstate the Thames towpath but often developers and residents of luxury flats do not want walkers passing through their grounds. As a result, security gates are locked and the route remains tortuous with the difficulties persisting from Wandsworth to Fulham.
The private Hurlingham Club in Fulham means another detour by road away from the riverbank. Factories play their part in making following the river difficult. In Wandsworth, for example, a large refuse processing plant has an overhead walkway, designed to be part of the route, but which is locked.
"The Thames Path has been one of the most troublesome trails in Britain," said David Else, who researched the path for Lonely Planet's Walking in Britain. "My impressions were mixed. Some sections were very good and others weren't signposted. When signs dribble out, it's quite easy to find yourself in a farmer's yard or in a sweet shop. The advice is to keep your eye on the map."