Blyth was born at North Berwick, East Lothian to Robert Brittain Blyth, an iron merchant, and his wife, Barbara, maiden name Cooper. He was their third son, and the first to survive to adulthood. Blyth was trained as a railway engineer under an apprenticeship with Grainger & Miller, a railway contractor. In 1848 he established an engineering practice on the prestigious George Street in Edinburgh where it would remain for the next 100 years. He took his brother Edward Lawrence Ireland Blyth into partnership in 1854, Edward having finished his own apprenticeship with Grainger & Miller, the practice became known as B & E Blyth. The practice did work for the Caledonian, Glasgow and South Western, Scottish Central, Dundee and Perth, Great North of Scotland and Portpatrick railway companies.
Blyth was a first cousin of Arthur Blyth, who was three times premier of South Australia in the 19th century. Their fathers were brothers.
Blyth died from diabetes agrivated by overwork at home in North Berwick on 21 August 1866 and is buried in Grange Cemetery, being survived by his wife, seven sons and two daughters. His eldest son Benjamin Blyth II took over his father's practice and the company remains in business to this day as Blyth and Blyth. His house served as the offices of Scottish Natural Heritage between 1950 and 2003 and will now be converted into apartments.