The destruction of Britain's railway network in the 1960s was a disaster for millions of people. But now, as Simon Calder discovers, some of the old routes are being reclaimed

Deep in the heart of Somerset, a strangely straight path leads southwards from the river Yeo. On either side, a tangle of undergrowth and overgrown trees could convince you that you have somehow stumbled through a space-time hedgerow and ended up in darkest Peru – a sense amplified when you peer through the verdant muddle and discover evidence of ancient masonry.

These strange slabs are not the work of the Inca Empire, but of an even more creative force: Britain's Victorian railway builders. This is all that remains of Congresbury station: one of thousands of halts across the UK that were, in the 1960s, considered surplus to transportational requirements. The mesh of untidy twists and knots that suffocate the platforms at Congresbury makes it clear that this particular patient will never be resuscitated.

Besides, the "Strawberry Line" that runs from the main line at Yatton south-west through crumpled countryside towards Cheddar has been reborn as a 21st-century amenity. It is now one of Britain's most rewarding railway paths: walkers and cyclists can gently traverse some of Somerset's loveliest countryside through a delicious sequence of embankments and cuttings – plus a damp tunnel where you may imagine you hear the echo of a distant locomotive. Or perhaps it's just a truck on the nearby A38.

I pedalled the path this autumn while making a television programme about Dr Richard Beeching's vision of a new Britain, in which the railway network would be all the healthier for the elimination of "those parts of the system which are obviously unsound". Survival of the fittest might work as a strategy for nature – but for a man-made network on a small, densely populated island, the wholesale amputation of lines has proved a disaster for the nation's infrastructure. And nowhere illustrates that better than Somerset.

It's great, and it's western: Somerset, despite having bits lopped off in various boundary reconfigurations, remains one of England's most diverse and beautiful counties. Only one problem: how do you get around?

One fine Monday morning in September, I set off on a journey from the north coast of Somerset to the far west of the county – not for a nostalgic celebration of steam, but to see how tricky it is to get around without getting stressed or trashing the planet. The trip I made, from Portishead to Minehead via the pretty town of Cheddar and the hauntingly beautiful Somerset Levels, would have been a piece of cake until 1964. For a start, regular trains trundled from Portishead to Bristol Temple Meads in just over half an hour. Not any more.

I joined a commuter, Lisa Metcalfe, in Portishead, this coastal community with ambitions to be north Somerset's answer to the South of France. It boasts a marina with shops, restaurants and a certain sense of glamour. But the railway station was erased some years before Lisa was born, so she makes the 12-mile journey to her job with the Soil Association in Bristol by car. Very slowly. "It makes me want to cry," Lisa said, after we had spent just half an hour together.

As it turned out, the cause of her upset wasn't so much my company as the appalling traffic: in 30 minutes, we had moved less than a mile from her home. The 12-mile journey to the centre of Bristol took just over two hours. "I'm going to have to stay in town with a friend a few nights a week, so I can get to work on time."

I removed my folding bike from the boot of her car and set off for the most magnificent junction in Brunel's kingdom of the train, and the hub of the region's rail network: Temple Meads station. The trouble is, most of the spokes are now missing.

One that still exists is the main line south-west to Taunton, Exeter and Penzance. Dr Beeching concurred that the nation needed fast intercity trains – though it took an aviation magnate, Sir Richard Branson, to convince government of the need to provide regular "clockface" trains on the cross-country network. As you whizz through Yatton at 100mph, look east and you can make out the faint shadow of a branch line disappearing off to the left. This is the start of the Strawberry Line, which once transported children to school and soft fruit to the north of England, with equally gentle treatment for both. Were you to follow the path, you would stumble upon Somerset's own Machu Picchu, Congresbury station – which untidily sums up the damage wrought by successive governments to our once-glorious 19th-century infrastructure.

For some inglorious 20th-century infrastructure, stay on the express to Taunton, a once-noble junction now cloaked in shabby renovation. I arrived on an Inter-City train to discover that I had missed the last train to Minehead. By 37 years. The 26 miles between Taunton and Minehead comprised one of the last lines to be closed, with the final departure from Taunton leaving in January 1971. Yet, as with many stretches of line, the British passion for railways meant it was soon reopened as a "heritage railway". The West Somerset Railway is now one of the most successful in the UK. The same seductive mix of steel, steam and scenery that led to it being chosen for the Beatles' 1964 film, A Hard Day's Night, now attracts an average of 1,400 people a day in summer. Yet it reaches tantalisingly close to the national rail network, with a gap of just four miles between Taunton and the station at Bishop's Lydeard, now the terminus for a line to nowhere – sorry, to Minehead.

The holiday resort has been in the same realm of inaccessibility as Mali and Mongolia due to the surgical removal of the line by the Beeching Axe. If it were reconnected, the sinking fortunes of the seaside could be revived. As it is, you need a car – or a bike – to cover the ground.

It took me 20 uncomfortable minutes to cycle from Taunton to Bishop's Lydeard along the A39, passing a sign that warned "161 casualties in 5 years". Dr Beeching was never asked to take into account the cost of lives lost or shattered in road accidents, nor the damage wrought on communities. After huffing and puffing through tranquil countryside, and then grazing the Somerset coast, the train finally wheezed its way into Minehead.

As I surveyed this handsome resort, I sipped a cup of tea and wondered what they must have put in the politicians' tea, to bring about the collective transportational madness that descended on Britain in the 1960s. "I know," someone must have said at about the time that London's magnificent Euston station was being demolished, "let's build a supersonic airliner that will cause immense harm to the environment while transporting a very few very rich people across the Atlantic in half the time of a conventional plane. And, while we're at it, let's emasculate the rail network on which millions of ordinary folk depend."

Besides the ill-conceived Concorde, Britain has given the world much to be proud of: Shakespeare, football, folding bikes. But the greatest gift of all is the railway. Somehow, though, in the 1960s we let the wheels fall off: nobody blew the whistle on the all-stations departure to oblivion.

'Beeching's Tracks with Simon Calder' is on BBC4 at 8.30pm on Thursday 27 November

From Beeching to 'bustitution' to bikes

Poetry, but no motion: "Abbey Town, Acrow Halt, Acton Central, Addingham, Adlestrop..." The first five stations to be listed alphabetically on page 109 of the Beeching Report, under the heading "Passenger Stations and Halts to be Closed", have a wonderful rhythm that rattles through 13 pages, finishing "Yeovil Town, Yetminster, Yorton". If yorton – sorry, your town – has no station, it's probably due to "The Reshaping of British Railways", published 35 years ago.

Plus ça change: the economy was in a right old mess, and the railways – which had fewer passengers than they do now, were, in financial terms, a severe drain on the Treasury. The Conservative transport minister, Ernest Marples, brought in the technical director of ICI, Dr Richard Beeching, to transform Britain's railways.

He certainly did. "The changes proposed are intended to shape the railways to meet present-day requirements by enabling them to provide as much of the total transport of the country as they can provide well".

Marples, who had close links with a road-construction business, gave Beeching the narrowest of terms in which to consider the railways. He was to look only at the financial performance of each line, with no regard to wider social benefits, or the costs to society of closure. "Bustitution" was the sop offered to communities suddenly cut adrift; but replacement bus services were slow and unreliable, and rarely lasted.

Those with cars were expected to drive to the nearest station to get the train. In practice, though, once people get behind the wheel, they tend to complete the journey by car.

The dismantling of the network reached a peak in 1964, when more than 1,000 miles of track were closed. Labour came to power in October, and promised to roll back the programme of cuts; instead, it continued, and more miles of track were closed under Labour than by the previous Tory administration.

Some lines that were clear candidates for closure survived: the Mid-Wales line and the West Highland line were preserved thanks to political pressure. A few have been reinstated, and more reopenings are on the drawing board, such as the Galashiels-Edinburgh line.

Ironically, the enthusiasm for removing "duplicate" lines created the conditions for the National Cycle Network to take root. One of the links between Bristol and Bath was resurrected by the Sustrans charity as the prototype for safe cycle paths across the country.