Robertson was an industrialist, working in many areas of engineering including railways and bridge building. He was also an original member of IMechE. In North Wales he completed viaducts and structures, such as the Queensferry Railway Swing Bridge. As a civil engineer, he built railways all over Wales. Robertson was a co-founder of the renowned locomotive manufacturers Beyer, Peacock and Company; a sleeping partner, his connections proved invaluable.
He served as Liberal MP for Shrewsbury from 1862 to 1865 and from 1874 to 1885, and Merioneth from 1885 to 1886, resigning his seat as a result of his opposition to the Home Rule Bill (for Ireland).