The son of William Cudworth, Chief Engineer of the Stockton and Darlington Railway. Born at Darlington in 1848, and, as a member of the Society of Friends, received his education partly at Stramongate School, Kendal, and partly at Bootham, York. In 1865 he entered the service of the Stockton and Darlington Railway Company - a section of the North Eastern Railway - as a pupil under his father. Served as chief assistant under his father and Mr. Joseph Cabry, on the central division of the North Eastern Railway from 1874-1891. Cudworth was later appointed Chief Engineer of the enlarged southern division, with headquarters at York. He was also responsible for the extension of the Hartlepool docks and of the Wear Valley Railway; the construction of the new Durham coast-line connecting the Hartlepools and Seaham, and Isle of Axholme Joint Railways, the latter including a swing-bridge across the South Yorkshire Navigation; and, finally, the Selby and Goole Railway. Cudworth was elected an Associate Member of The Institution on the 6th March 1883, and was transferred to the class of Members on the 7th January, 1896. Between 1903 and 1906 he served as a member of the Council. He died aged 61 at his residence, Butts Close, York, on the 31st December 1909.