The eldest son of the Rev. William Horner, a Wesleyan minister, Horner was born in Bristol. He was educated at Kingswood School, a Wesleyan foundation near Bristol, and at the age of sixteen became an assistant master there. In four years he rose to be headmaster (1806), but left in 1809, setting up his own school, The Classical Seminary, at Grosvenor Place, Bath, which he kept until he died there 22 September 1837. He and his wife Sarah (1787?–1864) had six daughters and two sons. One of the sons, another William Horner, continued to run the school. He, too, had a large family; the youngest were twins, Charles and Francis John Horner (1852–1887). Francis Horner matriculated at St. John's College, Cambridge in 1872, taking out a BA in 1876 and an MA in 1883. He became a lecturer in mathematics at the University in Sydney, where he died after only a few years - he had been advised to try a change of climate on account of tuberculosis.