When did English become a major subject in Japanese schools?

The teaching of English started in the early 19th century due to British incursions, particularly the Phaeton Incident (French studies started at the same time, due to Russian incursions as French was the language of the Russian upper class who attempted to contact and trade with Japan). Initially, the Dutch interpreters in Nagasaki tried to learn from a few Dutch merchants who had some English, but this was not entirely successful. Shipwrecked sailors were the next best source of English, although the extent of this teaching source is not known. The most famous of these 'teachers' was Ranald MacDonald who taught for around 6 moths in 1849. He had a very positive experience in Japan according to his testimony to the US congress at a later date.

Serious widespread English studies started in the 1870s when individual regional lords were competing for influence in the new era promulgated in 1868. When domains were abolished in 1973, the new central government took control and English education initially reduced and then increased when it was chosen over German and Chinese (Mandarin) as the preferred foreign language after the Imperial rescript on education was promulgated in the late 1880s.

From this time onwards English has been the preferred foreign language in education although other languages are also taught, including Mandarin, Korean, French, German and, in specialist schools, other languages from around the world.

In 1989 it was stipulated that English should be taught for communicative purpose, although no measures were taken to achieve this aim. In 2003 the government took major measures to retrain English teachers and reform the curriculum, which appears to have had some success. In 2013, it was stipulated that all English lessons should be taught in English in state run schools. There has been little research done on whether this has been implemented or not.

Teaching of English became universal starting in elementary school around 1910. Here is a summary of the history:

This was the situation in 1872 the year after the Daimyos were disbanded:

While on the subject of education, I may mention that there is among the Japanese of all classes, an universal desire for acquiring foreign languages, especially English, and other branches of learning. The principal establishment where foreign instruction is given in Yedo is the Kaiseijo (school) under the superintendence of the Rev. Mr. Verbeck, an American missionary. The number of pupils is about 400, of which 200 are instructed in the English, and the other 200, in about equal proportions, in the French and German languages. The number of foreign teachers is fourteen, besides Mr. Verbeck, namely, four Americans, three English, four Frenchmen, and three Germans.

Vice Consul Dohmen to Mr. Adams, Yedo, February 15, 1872
Commercial Reports from Her Majesty's Consuls in Japan [note Yedo means the city we now call Tokyo]

Thus in Tokyo we have 400 English students in a nation of 16 million people, but a "general desire" to learn English and other foreign languages.

This was the situation in 1889:

The demand for an English education in Japan is, and has been for several years, so great that all the native and missionary schools combined are unable to meet it. The young men and women throughout the land, in the towns and cities not only, but also in the remotest mountain districts, are extremely eager to learn enough English to be able to read, and many are ambitious to speak the language as well as to read it. The Japanese government has done much to meet this great and ever-increasing demand.

"English in Japan" by the Reverend T.T. Alexander in Osaka
The Church at Home and Abroad, Sept. 1889

English teaching begins to be widespread in private institutions, but is not government sponsored.

By 1904, due to the Sino war, English teaching became standard in "middle schools", a type of university in Japan. (see Japan by the Japanese: A Survey by Its Highest Authorities edited by Alfred Stead, 1904). There were 26,000 students in about 250 middle schools at that time. This standardization of the subject in colleges resulted in the spread of the curriculum in lower schools, so that English teaching became general by about 1910:

All these boys of Japan are filled with the liveliest interest and wide-eyed curiosity about America and England. All would like to write letters to American boyx, for English is taught now in every high school and every grammar school in Japan.

Letter by Dr. Jordan of the Boy Scouts of America who travelled to Japan in 1911
Boys Life, June 1915