The Ladd Company
The main producer for Blade Runner was a British guy named Michael Deeley, who also worked on the original Italian Job (1969) and The Deer Hunter (1978)—so he had some cred. Warner Bros. was the distributor, but the production company behind the film was the Ladd Company—which was actually responsible for an eighties mega-hit, the Academy Award-winning Chariots of Fire (1981). They also did the less successful Sean Connery space western Outland (1981).
Since it initially confused everyone, it obviously took time for Blade Runner to pay off—but now, it clearly has. Ladd went on to produce other successful flicks like The Right Stuff (1983), and Braveheart (1995).
Got the Clearance to Run Your Interference
Did the producers insist on messing with the movie? Oh, yeah. After test audiences were perplexed and had trouble following the story, the film's financial backers, Bud Yorkin and Jerry Perenchio, forced Harrison Ford to record a voiceover track. Ford agreed, recorded the lines they gave him, and found himself hating the new narration.
While initially not opposed to the idea entirely, Ridley Scott was also displeased with the voiceover, which contains lines like: "Sushi—that's what my wife used to call me. 'Cold fish.'" (You may have seen this version yourself. Some people don't think the voiceover is all that bad, really.)
Ford and Scott thought the narration was just a little too hammy, a little too reliant on film noir private-eye clichés, and in the "Director's Cut" and "Final Cut" versions of the movie, Scott was able to remove the voiceovers.
The revised versions also generally make Deckard and Rachael's future appear much more ambiguous and uncertain. As for other changes, Yorkin also insisted on altering the ending, going for a more conventional happy Hollywood version.