Green’s Dictionary of Slang

the last minutes of proper night-time, when darkness is gradually giving way to dawn.

1886		Daily News 12 Oct. in Ware (1909) 38/1: The birdcatcher has often to be up ‘at blue o’clock in the morning.’ The rime is on the grass when he lays his nets. It is bitteerly cold standing about in the fields.
1909		J. Ware Passing Eng. of the Victorian Era.
1917		C.T. Cade Dandelions 54: Blue o’clock in the morning is a silly hour to be out of one’s bed; still the pre-dawn sky was very beautiful as the black gave way to purple.
1922		Joyce Ulysses (1961) 234: It was blue o’clock in the morning after the night before.
1962		B. Spicer Act of Anger 14: He should not have gone dashing off on a mysterious errand of mercy and left her stranded at the Callisons’ party until blue o’clock in the morning.
2014		M. O’Sullivan Sleeping Dogs [ebook] Quarter to twelve but it still felt like blue o’clock in the morning in the windowless ICU ward.