I know that all Englishmen drop some "h"s but many drop only a few. My guess is that you don't drop the leading "h" in hypothesis (or history, or hotel ...). If so, your use of an expression such as "an hypothesis" is therefore, I put it to you, silly.
But one does, in fact, drop this particular aitch - so taint silly...
Actually, according to Google Ngrams, "a hypothesis" overtook "an hypothesis" in popularity even earlier in Britan than in America (in 1895 and 1934, respectively).
As editor of a journal with Hypotheses in its title, and reviewer of about twenty hypotheses per week, I got fairly used to using this word - it became a habit. I think I picked it up from seeing John Betjeman on TV when a teenager - he always used to say "an 'otel".