Graham's father was the founder of a firm, and in 1810 W & J Graham & Co diversified its business interests when it began importing wines from Portugal. Graham's became one of Britain's most prominent port shippers. Graham was a moderate Liberal, who was elected on 14 July 1865 with Robert Dalglish in Glasgow. He was re-elected in 1868 with Dalglish and George Anderson in the party's great Glasgow triumph in the general election of 1868 when Glasgow's electoral representation was raised from two to three MPs. Graham was a friend and patron of Edward Burne-Jones since 1856. Graham bought several of Burne-Jones's works and the 1886 sale of his collection allowed new Burne-Jones enthusiasts to acquire coveted pieces. Graham also invited artists such as Burne-Jones and Edward Clifford to his country house, Stobhall, in Perthshire. Clifford in turn acquired three paintings from Graham's collection in 1886. At Rossetti's persuasion, he commissioned Found for 800 pounds in 1869; the painting remained unfinished, and took possession of the work after the painter's death in April 1882. In 1871, Graham commissioned The Blessed Damozel from Dante Gabriel Rossetti. He also acquired from the artist. Graham began to buy from Rossetti in the mid-1860s. When they came on the market in 1874 and 1885, Graham bought his two Pre-Raphaelite Brotherhood oils, Ecce Ancilla Domini and The Girlhood of Mary Virgin both now in the Tate Gallery. He also commissioned the large Dante's Dream, although this was found to be too big for his London house. Many of the pictures he owned are now in Tate Britain. From Edward Burne-Jones, Graham also acquired many pieces. In the 1870s, Graham commissioned the two large oils Laus Veneris and Chant d'Amour, which were the most important items in a large collection of Burne-Jones's work, formed from the mid-1860s. The Graham piano was painted by Burne-Jones for Graham's daughter Frances ; Frances continued her father's role as friend and patron of Burne-Jones. William Morris and Burne-Jones also prepared a copy, one of four, of The Rubaiyat of Omar Khayyam for Frances. His importance is not only as a purchaser and a patron, but also as a person whose fine collection of early Italian paintings helped to inspire the artists whom Graham supported such as Rossetti and Edward Burne-Jones. After his death, his collection was sold at auction by Christie's in April 1886.
Issue and descendants
Graham married Jane Catherine Lowndes, and had issue including:
# Barbara Jekyll, married first 1911 the Hon. Francis McLaren, M.P., who was killed in 1917 in the War, and, secondly, in 1922, Colonel B. C. Freyberg, V.C., later Lord Freyberg, and had issue by both husbands.