Duckworth was the second son of Robinson Duckworth Sr. of Liverpool and his wife Elizabeth. He was educated at the Royal Institution School in Liverpool, and later at University College, Oxford, where he took his BA in 1857. He was a member of the Oxford Choral Society and a renowned singer. He took his MA in 1859, and his BD and DD in 1879. He was an Assistant Master at Marlborough College from 1857 to 1860. From 1860 to 1876 he was a Fellow of Trinity College, Oxford, where, from 1866 to 1870, he was Instructor and Governor to Prince Leopold, Duke of Albany, Queen Victoria's youngest son. In 1864 he was appointed Examining Chaplain to the Bishop of Peterborough.