That's the Armstrong Whitworth (AW660) Argosy surely? And since those R. Da. 10s are putting out considerably more horse power than the R. Da. 7s of my Dart Herald experience, I would venture that they're not whistling in that mode of flight, and forward of the compressors, but BLARING MIND-NUMBINGLY. Unless the sound-proofing on the Argosy flight deck was a whole lot better than in the Herald, which wouldn't be difficult, come to think of it.
If I remember correctly Armstrong Whitworth morphed into Whitworth Gloster in 1961. The Argosy flight deck was noticeably less noisy than the the dart Herald as the engines were farther away and the sound proofing more efficient, but I do remember the distant, but ever present whistling noise.