Songfacts®:

• Of the three instantly recognizable war songs Coward penned during the second great conflict of the Twentieth Century, this is the most easy going. "Could You Please Oblige Us With A Bren Gun?" is an obvious satire on the Home Guard.
  On May 14, 1940, a British Government broadcast appealed for men to serve as Local Defense Volunteers; the name was changed to the Home Guard three months later. Most able-bodied men were already serving in one of the forces; the few suitable civilians left were either very young, too old, or in reserved occupations. In any event, by the end of June there were over a million applications; the volunteer force was not disbanded until the very end of 1945, though as might be expected, and as the song emphasizes, the quality of its volunteers was the least of the Home Guard's problems.
  Unsurprisingly, the new defence force became known as Dad's Army, and was immortalized in a BBC comedy TV series of that name which ran for eighty episodes between 1968 and 1977. Coward's song would have been an excellent theme for the series, but its co-writer Jimmy Perry came up with something just as suitable in "Who Do You Think You're Kidding, Mr Hitler?"
• The hero of "Could You Please Oblige Us With A Bren Gun?" was originally
  "Colonel McNamara who
  Was in Calcutta in '92."
  
  But Coward changed the name to Colonel Montmorency when it turned out that there was a Colonel McNamara working for the War Office who had indeed been in Calcutta in '92!
• The song itself is in 6/8 time, and very cleverly constructed with the trademark Coward internal rhymes. It was first used by the man himself on July 13, 1941 at the Hammersmith Palais de Dance, and later when he entertained the troops. The sheet music was published the same year, by Chappell of London. >>

  Suggestion credit:
  Alexander Baron - London, England, for above 3