Well, Chambers Twentieth Century Dictionary (published in Edinburgh and my standard reference for clear and current British Isles English, as well as elegent definitions) gives both "diarrhea" and "diarrhoea" as alternative spellings, without indicating a preference for either.

The OED, while giving "diarrhoea" as the primary spelling, also offers both "diaria" and "diarrhea" as alternatives. Indeed, the first usage examples that the OED provides are of "diaria" (in 1495) and "diarrhea" (in 1544). Only in the 1564 example does "diarrhoea" show up.

To be clear, though, the Latin root is indeed "diarrhoea" and the prior Greek root is similar. But the British started screwing up Latin and Greek long before colonial times. Probably has something to do with the degredation and declining academic standards of the schools in the 15th century.