The Dulwich Picture Gallery has in its collection a scene of Venice by the celebrated Italian painter Canaletto. Painted in oil on canvas in 1760, it shows the Venetian state barge, covered in gold-leaf, about to dock near Piazza San Marco during the city-state’s Ascension Day celebrations. Fine examples of Venetian architecture loom grandly over the water, depicted in such detail that even a partial view of Saint Mark’s Basilica in the distant background boasts the precision of an architect’s drawing.

Anyone familiar with scenes like this by Canaletto will find a fascinating contrast in a Venetian scene created by the Japanese artist Yoshida Hiroshi (1876-1950), currently on show as part of the gallery’s new exhibition, Yoshida: Three Generations of Printmaking. It has a livelier, more rustic feel than the Canaletto, and not just because the place of the Venetian state barge is taken by a handful of humble gondolas. This is a woodblock print: a medium intimately associated with simple, vibrant scenes of early modern Japanese life in cities such as Edo (now Tokyo). One expects to encounter sumo wrestlers, courtesans, kimono-clad women crossing rainbow bridges and idyllic views of Mount Fuji. So there is a certain joyful dissonance in finding woodblock printing used to capture a quintessentially European scene. For many, standing in front of this image, there will be instant recognition, too: such is the extraordinary global influence enjoyed by the woodblock print aesthetic since western artists and collectors began taking an interest in the late 19th century, supercharged in recent decades by Japanese animators such as Miyazaki Hayao using bustling pre-modern European street scenes as part of their rich fantasy worlds.

Yoshida Hiroshi would no doubt have approved of responses like these to his work. Born into a lively period for Japanese culture, as Western and Japanese artistic ideas mixed and mingled, he set out to bring some of the Western techniques in which he trained as a young man – oil, watercolour, sketching – to his later work as a print artist. Some critics in Japan dismissed woodblock printing as too closely associated with the country’s ‘backward’ early modern era, but woodblock artists found a ready market for their work nonetheless, both at home and abroad. And whereas in the past they had had to share their profits with woodblock carvers and publishers, they could now oversee the whole creative process themselves. A ‘new print’ (shin hanga) movement began to emerge, in which Yoshida Hiroshi took a leading role.

The prints on show at this exhibition, the first in the UK or Europe to offer a retrospective of the Yoshida family’s contribution to woodblock printing, show Hiroshi bringing international inspiration of all kinds to his work. He travelled widely in Asia, the United States and Europe – including a visit to the Dulwich Picture Gallery in 1900, where he signed the visitor book – and he was especially a fan of dramatic landscapes. Visitors will find charming prints of the Grand Canyon, Swiss mountains, Athens at night and Egypt’s Great Sphinx. European impressionists like Monet were influenced by Japanese woodblock art, and in some of his prints Hiroshi seems to be repaying the compliment by drawing on the Impressionists. Where Monet’s Haystacks series depicted its subject in differing lights and atmospheres, Hiroshi achieved a similar effect by printing images such as The Sphinx using different colours, capturing it by day and night.

Hiroshi’s Japanese scenes are likewise indebted to modern European techniques, but the effect here is rather different. There is a whiff of nostalgia about some of these pieces, not least his Twelve Scenes of Tokyo. Kameido Bridge, seen through blooms of wisteria, calls to mind the vanished world of Hiroshige’s One Hundred Famous Views of Edo (1856-8). Kagurazaka Dori is a more modern scene, but the blur of electric shop- and street-lighting reflected in a wet street after a downpour lends the image a quiet, timeless quality.

Hiroshi’s wife Fujio trained in Western art, too, and in 1903 became the first Japanese woman artist to have her work exhibited in North America. She worked in oil, watercolours and then woodblock print, becoming known after Hiroshi’s death for abstract close-ups of flowers – some of which feature in this exhibition. Their son Tōshi, on whom fell the responsibility of reviving the family workshop’s fortunes after the Second World War, produced both traditional views, as his father had done, and also more abstract images, of which his father apparently disapproved. Striking in the latter vein are Woman in Baghdad, comprised of starkly simple shapes resembling pieces of stained glass, and Frontier, which shows enormous rock formations inspired by Arizona and Utah looming over a dimly-lit cityscape in the foreground.

Both Tōshi and his brother Hodaka carried on their mother and father’s approach of travelling widely and feeding the scenes and cultures they encountered into their work as woodblock print artists. Hodaka’s debt to Mayan art comes through in Profile of an Ancient Warrior: an abstract scramble of whites, blacks and reds, in which fun can be had trying to make out the samurai’s top-knot and sword. Where Hodaka’s interest in Pop Art leaves some of his prints feeling a little derivative, his wife Chizuko’s work has great energy to it. Jazz is a riot of swirls and zig-zags, with thin black oblongs off to one side suggesting a piano keyboard exploding into life. Her aerial view of Tokyo combines woodblock printing with photo-lithography to create a classic view of the metropolis, steadily disappearing into the haze of the rainy season as your eyes move up the image.

Chizuko and her mother-in-law Fujio were both active promoters of female artists, in a world dominated by men. Fujio was one of the founders of the Vermilion Leaf Society in 1918, the first association of female artists in Japan. Chizuko joined the Society in the 1940s, and later co-founded the Women’s Print Association. It is a pity that given Japan’s dramatically shifting politics, from the 19th century through to the present day, the family’s oeuvre doesn’t have a little more edge to it. Katsushika Hokusai (1760-1849) once conjured a memorably malodorous verdict on lazy and obsequious members of his country’s samurai class: a senior samurai sits on a toilet, his face a picture of blissful relief, while three of his retainers crouch on the ground outside, holding their noses. Yoshida: Three Generations of Printmaking is altogether more respectful, both of the Yoshida family itself and of Japan’s turbulent modern history. The work here is often beautiful and sometimes intriguing. It is also rather safe: there is a sense that across these decades, art as commentary and as social or political challenge must have been happening elsewhere.

Instead, where this exhibition succeeds brilliantly is in showing us how a single family took a genre that first flourished in the early modern era, and helped it not just to survive but to evolve. We move from the ancient and the elegiac through the influence of international landscapes, Impressionism, modernism, abstraction and on into Chizuko’s innovative use of photo-lithography. We finish with a third and final generation of the family: Yoshida Ayomi, daughter of Hodaka and Chizuko. Her work is taking woodblock culture in still-new directions, including the use of chips and shavings created during the woodblock carving process. A giant cherry blossom installation, created especially for this thoroughly enjoyable exhibition, showcases her techniques and brings an exhilarating, uplifting family journey to its conclusion.

Yoshida: Three Generations of Japanese Printmaking is at Dulwich Picture Gallery until 3 November.