This is a bit of a misnomer that's arisen from modern census questions. If you combine the number of americans descended from english, Scottish and scotch-irish backgrounds i believe that number is greater than german-americans. The difference is there is no overall "british" listing on the census or most americans of those groups would not list themselves that way.
Not to mention at the time most political leaders in washington as well as many financial ones were of a british background anyways.
I think another problem - at least one I found first learning about this stuff as a youth and which may be common with AH lovers - is that there is a tendency to confuse this situation with the Anglophile/Francophile debates of a little over a century earlier.
Back around 1800, both nations were impressing seamen, both were seeking the U.S. as a friend - I mean, the French ambassador even promoted Jefferson in 1796, his interference not occurring is the POD for my "Created Equal" TL. The first political parties took shape partly because of the debate, as well as other things, of course. There was real question as to who the United States was, like an adolescent considering their place in the world - would they support the monarchy or the radical revolutionaries?
But, by the 1910s, you had none of these things. Britain was an established friend, though relations were a bit cooler at times there were, to my knowledge, no major sentiments that the U.S. should abandon Britain and go full-steam toward a German alliance. While there were many German-background Americans, they were not the Francophiles of 1800, they might be proud of their heritage, but they had a definite love of democracy over the land which their ancestors had left, sometimes many decades earlier.
Or, maybe I'm the only one who ever tried to make that connection.

But, it's not there.