I'll try to answer your questions in the order you put them.
I can't tell where in the UK my Easums came from. I can only trace them back to around 1800, to Mathew Esum [sic] in the parish records of St. Dunstan's, Stepney, Middlesex. I don't believe the family is originally from the London area, althoughwhat has been made available online seems to indicate thatEasums were there already perhaps for hundreds of years. There may have been a long connection with East Sussex: "Arundel" and "Chichester" [poor kids] show up as middle names in my great-grandfather's generation. After Geoffrey and [my great-grandfather] Basil came to Canada in the early 1890's they adopted the honorific "d'" which had not been used for four centuries. [ It would be intersting to see if any court records can be found in which they support their claim. Otherwise, it must have seemed a little indecent to the rightful claimants of such titles. Perhaps the Crown held standards for proof.] I don't think the derivation of "Isham" is disputed. The name of the river Ise is now, I think, pronounced "eyez": the "I" is long. I don't think that this pronunciation has been constant. Eilart Ekwall suggests in one or other of his works on English place names that the name of the river is akin tothat of another nearby, the Ouse. Although I don't know anything about the languages and dialects of early medieval England, the vocal shift from Ou- to I- ("ee-") seems to me to be more plausible than one to I- ("eye-"). Obviously, such questions are better taken up by those who are qualified. Genealogy is not something I can devote much time to: my research comes mostly when I'm procrastinating.Exams begin on Monday.