What's the meaning of the phrase 'Blue funk'?
Either, in the UK, a state of extreme nervousness or, in the USA, despair.
What's the origin of the phrase 'Blue funk'?
Two versions of the expression 'blue funk' exist and were coined separately. The UK 'in a state of nervousness' meaning was coined there in the 1850s. The US 'state of despair' version was coined much later, in the mid-20th century. Of course, to know how both came about we are going to need to know what 'funk' meant in 19th century Britain and 20th century America. That's not as easy as it might be; the OED lists ten different meanings of the word - six as a noun and three as a verb.
Taking the UK version first, the funk referred to there meant 'a state of anxiety'. The 'blue' is just an intensifier. An early example of the phrase in print is found in the anonymous English novel Phrenologist's Daughter, 1854:
Stapleton was in a blue funk.
In the USA a funk was 'a state of gloom'. This meaning was imported into the USA from Scotland where it had been in use since the late 18th century. In this case 'blue' as well as being an intensifier 'blue' doubled as a synonym for 'funk'. This version of the phrase was defined in The Daily Intelligencer, February 1958:
A Michigan reader reports that last winter she found herself in a long period of low energy and ‘blue funk’... It seems evident that ‘blue funk’ in this instance means merely low in spirit, gloomy, melancholy, pensive, moody.