Engel was born in Thiedenwiese, near Hanover, and studied the pianoforte under Hummel.
He owned a large collection of rare musical instruments, many of which were given after his death to the South Kensington Museum, with which he had been connected for many years.
One of his nephews (a son of his sister Elisabeth) was Carl Peters (1856–1918).
Engel later committed suicide and bequeathed his fortune to Peters.
Among them may be mentioned: An extensive account of the musical instruments of the world was still unpublished in 1888.