Elliot was born in Gateshead, the son of a pitman. He worked at the Pensher mine owned by the Marquis of Londonderry (q.v.) and became an overman by 1837. By 1844 he was manager at Wearmouth, then the deepest mine in Britain, and it was not long before he moved into mine ownership. He later extended his holdings to Wales, Staffordshire and Nova Scotia. A wire-rope business he had bought in 1849 was responsible for the first transatlantic cable in 1866 (v. SIR DANIEL GOOCH).
Elliot was a new type of mining engineer, whose expertise went far beyond mining itself. He helped to found the Institute of Mining Engineers in 1852 and was its president in 1868-69. He was in the forefront of experiments in mining technology and safety, arguing that economy, safety and efficiency were compatible. Unlike many of his colleagues, he supported the establishment of a Mines Inspectorate.
Elliot's attitude to labour changed from being a Tory paternalist, advocating model villages provided by employers and condemning trade unions, to a conservative, believing in self-help and free collective bargaining. He was also, however, an early advocate of 'gas and water' socialism. In 1893 he proposed a kind of semi-nationalisation to solve the economic and labour problems in the coal industry. He was elected MP for the constituencies of West Durham, East Durham and Monmouth between 1868-92. Elliott had a London residence, two country establishments and belonged to four London clubs. Nevertheless he was not a model of social refinement and was known to his constituents as 'Bonny Geordie'.
Among all his other activities, which included building developments in Whitby, Elliott was also financial adviser to the Khedive of Egypt. In West Rainton church there is a stone from the base of the great pyramid of Gizeh, inscribed and built into the base of the spire by its builder, Sir George Elliot, in thanksgiving for his safe return from Egypt. At All Saints, Penshaw, there is another stone from the pyramid of Cheops inscribed in memory of the Elliots.