Spanning 1,450km from the North Sea to the Swiss Alps, the Rhine Cycle Route is 87% car-free, culturally rich and surprisingly accessible.

I blame Eurostar. And the airlines.

It's precisely because they make it so fiendishly tricky to transport a bicycle into Europe that I found myself pedalling the length of the Rhine for 1,450km (900 miles) from the Hook of Holland on the North Sea to the river's source high in the Swiss Alps.

Let me explain. My plan had been to join a friend cycling across the French Alps, starting on the southern shores of Lake Geneva and finishing at Nice on the Riviera. But the logistics of getting my road bike there – and home again – defeated me. So, I decided to ride it there instead.

In my Google search for quiet, car-free routes from London to Switzerland, I stumbled upon the Rhine Cycle Route, or EV15 – the first certified section of the remarkable 99,000km (61,515 mile) EuroVelo cycling network that is intended to criss-cross Europe by 2030. It already links locations as far flung as Trondheim in Norway to Santiago de Compostela in Spain and is likely to unleash tremendous interest in cycle tourism when it is completed. The Rhine route represents a milestone: 87% car-free, meticulously way-marked and open to everyone from Lycra-clad purists to families on e-bikes.

I was immediately intrigued. I could picture myself whizzing along the banks of the River Rhine on smooth tarmac, drinking in the myth and romance of a landscape contested since Roman times.

But there would be many other highlights along the way: the Dutch polders, side-trips to the Alsace Wine Route, the historic wooden bridges upstream of Basel, the Rhine Falls, Lake Constance, and, finally, the official source of the river high above a Swiss Alpine pass.

Unused to cycling with luggage, I vowed to travel light with one bag attached to my handlebars and a second to my saddle, weighing around 6kg (13lbs) in total. That meant wearing Lycra and carrying just one set of "civilian" clothing. Using a road bike with skinny 25mm tyres meant I would have a bumpy ride, but I judged it worth sacrificing comfort for speed. It would also be my first solo adventure in more than 30 years.

I had only 10 days to spare so would ride 145km (90 miles) per day, staying in reasonably priced hotels and hostels, rather than camping. I later learned that it doesn't have to be an ordeal – at least half of the long-distance tourers I saw on the route were riding e-bikes.

Where better to start than in the Netherlands, a cycling nation since the 1970s when a popular movement led to the country's roads being redesigned for bikes. At the Hook of Holland, where vast Stena Line ferries disgorge their passengers from Harwich, I gazed expectantly across the canalised expanse of the Rhine to the open sea. It was a sunny day in late August, and the beaches were busy.

Beautifully wide cycle tracks led me to Rotterdam, and I tucked in behind some speedy e-bike riders to shield me from the headwind. It took a while to adjust to the road rules in a country where the cyclist is king: it's no wonder that back in Britain, after Dutch-style roundabouts were built in places like Hemel Hempstead and Cambridge, a council had to issue a "how to" guide on YouTube.

It swiftly became clear that I had seriously misjudged the difficulty of covering such a long distance each day, and on the first night arrived exhausted at my hotel, east of Dordrecht, at 20:00. Although it was a Monday night, a wedding party........

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