He was the younger son of Jerom Murch (1807–1895), Unitarian minister at Bath, Somerset, and his wife Anne Meadows Taylor (1800–1893).

[5] He was sharing a studio in Great Russell Street, London in the later 1860s, with Frederick Jameson (1839–1916), but suffering from health problems.

[12] Arthur Murch married Edith Edenborough, who after his death remarried on 17 March 1891 to Matthew Ridley Corbet.

[15] Arthur and Edith had a son, Denis Jerom Murch, born at Venice in 1874.

Later in the Royal Artillery, he was left property in Sir Jerom Murch's will.