Anyway, Anglophilia in the United States had its greatest strength in the 1960's, with the "British Invasion" of popular music sparked by The Beatles. The British were never dramatically unpopular in the United States since then, except perhaps among older generations of Irish Americans, and even then the disdain was rather limited in its manifestation (my mom, for example, inherited her immigrant grandmothers' strong opinions on Ulster and the British role in the Potato Famine, but still gobbled up British music and television).
Japanophilia is really about a romanticization of the exotic and unknown, while British culture is too similar to the mainstream culture of the United States to strike a similar movement. The music of the British Invasion did initially have its own distinctive style, similar to Japanese cartoons in being a foreign reinterpretation of an aspect of American popular culture. Within just a few short years, however, the unique qualities of British rock music were in turn adopted by American musicians, to the extent that it can sometimes be difficult to tell what side of the pond a band or artist comes from. New styles of music have arisen on either side of the Atlantic many times since then, but they never really acquire a unique national identifier before they're consumed by the rest of the Anglophone world (just look at the emergence of the punk movement). Meanwhile, American animators and video game developers have certainly borrowed elements from the Japanese, but the large gap in culture and language will always distinguish the two.
I think an interesting topic would be whether or not another non-Western culture could strike a trend as successful as Japanophilia in the United States. Chinese, Russian, and Islamic World influences would be challenging considering the political environments from the second half of the 20th Century onward. Could a distinctively Korean, Taiwanese, or Malaysian form of entertainment emerge that is autonomous enough from Japanese pop culture? Perhaps something from India, Israel, Latin America, or anywhere in sub-Saharan Africa?