A lot of English surnames that start with D derive from Norman French owners of land. I knew a family originally called d'Alleguen who had dropped the D - this presumably dates from the late 18th cent. (the French Revolution), when it was more than anyone's life was worth to admit to a background among the landed gentry. This prejudice is very strong; I was working at a (holiday) language school in the early seventies, when my term-time French teacher (who was French) was Odette de Mourgues, and a French girl I told this was immediately hostile to her (not seriously, but the trace of a prejudice was still there).
You might start by following a few links from Name Meanings - Glossary of Surname Origins - D , but "Dalloway" doesn't seem to be listed there.