Born in Dundee, he was befriended by civil engineerL.D.B. Gordon. In 1838, whilst studying at the Freiburg School of Mines, Germany, Gordon visited the mines at Clausthal, and met Wilhelm Albert. Impressed by what he saw, he wrote to Newall, urging him to "Invent a machine for making wire ropes". On receipt of Gordon's letter, Newall designed a wire rope machine, consisting of four strands and four wires to a strand. On Gordon's return to the UK in 1839, he formed a partnership with Newall and Charles Liddell, registering R.S. Newall and Company in Dundee. On 17 August 1840, Newall took out a patent for "certain improvements in wire rope and the machinery for making such rope."
R.S. Newall and Company established a factory in Gateshead, England, and commenced making wire ropes for "Mining, Railway, Ships' Rigging, and other purposes". From this point forward, Newall was instrumental in developing substantial improvements to submarine telegraph cables, devising a method involving the use of gutta percha surrounded by strong wires.
The first successful Dover-Calais cable, laid in 1851, was manufactured in Newall's works, and approximately half of the Atlantic cable was also manufactured at his works. In 1853 he also invented the brake-drum and cone for laying cables in deep waters.
Newall was a keen astronomer, and he commissioned Thomas Cooke to build a telescope for his private observatory at Ferndene, his Gateshead residence. For many years, the 25 inch refracting telescope was the largest in the world, and it was gifted to the Cambridge Observatory after his death in 1889. By the end of the 1950s, the telescope had fallen into disuse, and in 1958 it was donated to the Penteli Observatory, at the time just north of the city of Athens.