Farrier was born in 1796 in Chelsea, London, and lived in that area throughout his life.
He was first placed for instruction under an engraver, but subsequently began to earn a living by painting portraits in miniature, and became a student at the Royal Academy. He first exhibited at the Royal Academy in 1818, sending some miniature portraits, and in 1819 exhibited the first of a series of pictures in a slightly humorous vein, depicting domestic subjects, and especially scenes from schoolboy life. These were popular, and a number of them were engraved.
The first which attracted notice was The Schoolboy—"He whistled loud to keep his courage up" (Blair"s Grave)— exhibited at the Royal Academy in 1824, and engraved by J. Romney.
Romney also engraved Sunday Morning—The Toilet (Research Associate 1825), Sunday Evening and The Declaration. Farrier occasionally travelled, but continued to live in Chelsea, where he died in 1879.
One of his pictures, The Parting, was presented after his death to the South Kensington Museum.