His first major work was the improvement of the medieval bridge at Rochester. The bridge was widened and the two central arches merged into one to provide a wider channel for shipping.[3][4] The work was not completed until 1824, by which time Alexander had been dismissed from his post as engineer to the bridge.[5] He was the principal architect of Dartmoor Prison and Maidstone Prison, two of the oldest gaols still in use in the United Kingdom.[6]
Point Alexander was named after him by Captain George Vancouver in 1793.[7]
In 1799 he carried out a detailed survey of Rochester Cathedral, and recommended a programme of repairs, which was begun in 1801.[8]
Alexander was the surveyor to the London Dock Company between 1796 and 1831 and was responsible all the buildings at the London Docks during that time, including the Pennington Street Warehouses and the London Dock House. The dock basins themselves were by the company's engineers, including John Rennie.[9]
^DeArmond, R.N. (2015). Southeast Alaska Names on the Chart and how they got there (Third ed.). Gastineau Channel Historical Society. ISBN9780986156991.