Liversidge was born at Turnham Green, Chiswick, England, the son of John Liversidge of Bexley and his wife Caroline Sophia, née Jarratt. Liversidge was educated at a private school and by private tutors in science, and in 1866 went to the Royal College of Chemistry and Royal School of Mines.
Liversidge became an associate of the School of Mines and in 1870 was awarded an open scholarship in science at Christ's College, Cambridge. In 1870 Liversidge became a demonstrator of chemistry at the university laboratory.