"SHQ" (Squadron Headquarters) must be the original. "AHQ" (Air Headquarters Iraq and Persia") was established at Shaibah (near Basrah, Iraq) in 1942. The base ("RAF Shaibah") was built in 1920.

I have another version that does begin "A little piece of bullshit fell." Instead of Bristol bombers, there are "Wimpeys" (Wellingtons).

"The blue" = the desert.

The chorus ends, "I'm fed up, and I'm fucked up, and I'm blue."

Otherwise, nearly identical.

Obviously the two stanzas could be sung without the chorus at places other than Shaibah.

There is also a World War II version of "Scapa Flow" that begins "a little bit of shit and muck...."