Henry Robinson was educated at Horatio Russell's academy in Ludlow until he was thirteen when he took a year's drawing tuition with Richard Penwarne before being apprenticed to a Ludlow bookseller and printer, Richard Jones.
In 1850 working for the Bromsgrove bookseller Benjamin Maund, then in 1851 for the London-based Whittaker & Co. In 1852 he began taking photographs, and in 1855 opening a studio in Leamington Spa, selling portraits. In 1856, with Rejlander, Henry Robinson was a founding member of the Birmingham Photographic Society.
In 1864, at the age of 34, Henry Robinson was forced to give up his studio due to ill-health from exposure to toxic photographic chemicals. Relocating to London, he kept up his involvement with the theoretical side of photography, writing the influential essay Pictorial Effect in Photography (1869), Being Hints on Composition, and Chiaroscuro for Photographers, published in 1868. Around this time his health had improved sufficiently to open a new studio in Tunbridge Wells with Nelson King Cherrill, and in 1870 he became vice-president of the Royal Photographic Society. He advocated strongly for photography to be regarded as an art form.
The partnership with Cherrill dissolved in 1875, Henry Robinson continuing the business until his retirement in 1888. Following internal disputes within the Photographic Society, he resigned in 1891 to become one of the early members of the rival Linked Ring society, in which he was active until 1897 when he was also elected an honorary member of the Royal Photographic Society.
Henry Robinson died aged 70 and was buried in Tunbridge Wells in early 1901.
Henry Robinson was an honorary member of the London Photographic Society (1871) and a founder/member of The Linked Ring (1892).
In 1859 Henry Robinson married Selina Grieves, daughter of a Ludlow chemist, John Edward Grieves. His son, Ralph Winwood Robinson, was also a photographer.