The Imperial Japanese Army and Navy were chiefly responsible. In the 19th century, Japanese cuisine was regionalised, and varied greatly between rural areas and towns and cities, and between rich and poor. Large numbers of young men from around Japan, from different backgrounds, passing through the army and navy helped build a more uniform national cuisine. For example, for many of these men, the army or navy was their first experience of a diet centred on white rice (have previously mostly eaten mixed rice and barley, or rice and millet, etc.). The army and navy faced many challenges when it came to feeding their soldiers and sailors. First, the regional diversity meant that it was difficult to find meals that would be acceptable to (almost) all. This was an important reason for their choice of white rice. Foods chosen also needed to keep well, and to be easy to cook, and with enough calories and other nutrients to sustain the soldiers and sailors.
With their dependence on white rice, with frequent shortages of fresh food, beriberi (vitamin B1 (thiamine) deficiency) was a problem, especially for the navy (in the Russo-Japanese war of 1904-1905, the Japanese suffered 27,000 beriberi deaths, compared to 47,000 combat deaths). Takaki Kanehiro, a medical officer in the navy, investigated, and on implementation of his recommended changes to the diet, reduced the beriberi rate in the navy by a factor of 300 in 2 years (Hawk, 2006). One of these changes in the diet was the introduction of curry as a regular meal in the navy. Curry fulfilled many needs for the navy. First, it provided improved nutrition and reduced the beriberi rate. Second, it was cheap - as a stew, it allowed the use of lower-quality and cheaper cuts of meat. Third, the curry powder provided plenty of flavour even if the other ingredients were quite bland. Fourth, it was acceptable to men from around Japan. Fifth, it was a Western dish - and British at that - at a time when the navy wanted to introduce Western dishes into their menu. The Japanese had recently (1870) decided to base their modernisation of their navy on a British pattern, and a British dish to add to their menu was well-regarded.
The origin of British curry was, of course, India, but it had been evolving away from the Indian versions for a long time already by the end of the 19th century. The earliest English-language curry recipe appeared in Hannah Glasse's 1747 book, The Art of Cookery Made Plain and Easy. By the 19th century, pre-mixed commercial curry powder was standard. Curries were often made with leftover roast meat, and featured British vegetables, and were often quite sweet (with apples and sultanas). It was such British-style curries that the Japanese adopted. One of the first books on Western cooking in Japan, Seiyō ryōritsū 西洋料理通 (The Expert on Western Cookery), 1872, included curry as an English dish.
Since curry appeared to work well for the navy for beriberi, the army followed suit and adopted curry as well. One difference between the navy and the army was that sailors ate what was cooked in the mess, and soldiers often cooked their own food. Thus, not only did large numbers of young men eat curry, they also learned to cook curry. Soldiers and sailors were not the only route by which curry spread throughout Japan - Japanese canteen cooking (school canteens, factory canteens, office canteens) was strongly influence by military cooking, and curry was a common canteen dish (Ashkenazi and Jacob, 2013). The military diet also influenced education about diet and nutrition in the 1930s and 1940s. These three paths together helped spread curry throughout Japan, and made it a popular post-war dish (Cwiertka, 1998; 2006). Of course, it also benefited from being tasty, cheap, and easy to cook.
Curry continues as a naval tradition, with curry still being the standard Friday dinner in the Japan Maritime Self-Defense Force. Individual ships have their own recipes (sometimes with secret ingredients such as coffee), and compete in an annual curry festival (Ono and Salat, 2013).
While the original adoption was in large part driven by beriberi, Takaki's theories were incorrect (B1 had not yet been discovered, so this is unsurprising). However, the roux on which the curries were based provided B1. An important contribution of mixed barley and rice to the diet was B1 from the barley; the wheat flour in the roux provides the same.
A brief timeline:
1747: Curry in England
1870: English curry reaches Japan
mid-1880s: Curry becomes a standard military dish
early 20th century: Curry entrenched in the military, and many sailors and soldiers are exposed.
1930s and 1940s; Curry in canteens, etc.
post-war: Curry becomes widely eaten.
Curry appeared as a restaurant dish already in the 19th century, but the military use of curry made it a popular dish.
References:
Michael Ashkenazi and Jeanne Jacob, The Essence of Japanese Cuisine: An Essay on Food and Culture, Routledge, 2013.
Katarzyna Cwiertka, "A Note on the Making of Culinary Tradition—an Example of Modern Japan", Appetite 30(2), 117-128 (1998)
Katarzyna J. Cwiertka, Modern Japanese Cuisine: Food, Power and National Identity, Reaktion, 2006.
Alan Hawk, "The Great Disease Enemy, Kak’ke (Beriberi) and the Imperial Japanese Army", Military Medicine 171(4), 333-339 (2006).
Tadashi Ono and Harris Salat, Japanese Soul Cooking: Ramen, Tonkatsu, Tempura, and More from the Streets and Kitchens of Tokyo and Beyond, Ten Speed Press, 2013
On Seiyō ryōritsū: https://blogs.bl.uk/asian-and-african/2015/03/japans-first-curry-rice-recipe.html