Japan’s new narrow-gauge wonder-train has proved so successful that it has completely sold out until April 2018 — despite a price tag that works out at up to £2 per minute. Even before the first run, on 1 May, demand has been so high that bookings have been allocated by lottery.

The Shiki-Shima is an extraordinary creation: a futuristic 10-coach train running on 3ft 6in-gauge lines and carrying a maximum of 34 passengers, who enjoy the most luxurious experience on the rails.

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The train is the latest excursion venture by the East Japan Railway Company. Its basic three-night/two-day “summer tour” starts from Ueno station in Tokyo. Lunch and dinner are served as the train rolls north to the mountain resort of Yuzawa and passengers acquaint themselves with the facilities on board.

Five of the 10 coaches are filled by the standard suites — three to a carriage, offer comfortable beds and a bathroom with shower and toilet. Another has just two “deluxe suites", each with an aromatic cypress wood bath.

There is also an observation car at either end from which to watch the scenery roll past, a lounge and a dining car with Michelin accreditation. Service on board is by uniformed butlers.

The name Shiki-Shima means “Island of Four Seasons”. Even by the standards of luxury trains, it is expensive: a solo traveller taking a standard suite can pay the equivalent of £7,500, which works out at £2 for every minute of the 60-hour trip.

The train's top speed is just 70mph, barely one-third of that achieved in normal service by some Bullet Trains in Japan. As with the new Japanese-designed trains for the Great Western Railway in Britain, it is equipped with both electric motors and diesel engines.

After dinner on the first night, passengers are given a live performance of the traditional Japanese “Dance of the Dead” — which the company says has been designated “An Important Intangible Folk Cultural Property".

The train rolls on through the night to Hachinohe, on the Pacific shore almost at the northern tip of the island of Honshu. Here, oddly, passengers transfer to a different luxury train, the Tohoku Emotion, which has “an open kitchen where you can watch your food being prepared while you wait”.

This train trundles along the coast to Kuji, where passengers disembark for a sightseeing trip.

The bedrooms are more like hotel rooms than train cabins (AFP/Getty Images)

After the return to Hachinohe and re-boarding the Shiki-Shima, dinner is served as the train meanders south to Naruko-onsen, a spa town set amid mountain scenery. After immersion in the “hot springs village”, passengers retire to their luxury suites.

The train slows to a crawl for the short overnight journey to Ichinoseki — prospective home for the International Linear Collider, a scientific research project which could help the search for dark matter. Passengers will be taken by bus to neighbouring Hiraizumi, home to a Unesco-listed temple complex.