Queen Elizabeth II
Edward did not have any legitimate heirs. Since Elizabeth's parents had no sons, who would have had precedence over her regardless of when they were born, she would eventually have become Queen whether Edward had abdicated or not, assuming she outlived her father.
our present queen would still have become queen because although a morganatic marriage was suggested to Edward VIII (ie any children of the marriage would not inherit the throne) a year after he married Mrs Simpson she had a hysterectomy...therefore our present Queen would have still acceeded to the throne