Snell was educated at the local school until he reached the age of twelve when he was hired at Newark Fair as an indoor servant for a farmer named Doncaster. Snell disliked his employer and left to work as a farm labourer.
After a while Snell found employment as a french-polisher in Nottingham. Although lacking education, Snell was intellectually curious and in 1881 Snell heard Charles Bradlaugh speak at a National Secular Society meeting in Nottingham. He later recalled that: "The impact of his personality reached me just at the moment when I was ready to respond to any plausible call to service, and my capitulation to his resounding appeal was immediate and enduring. I have never been so influenced by a human personality as I was by Charles Bradlaugh." Snell joined the National Secular Society and became an avid reader of the National Reformer.
Snell no longer believed in the "verbal inspiration of the Bible, in miracles, the biblical story of creation" but he retained a strong interest in religion. Snell was now attracted to the the local Unitarian chapel because of its "scholarly approach" to these issues. Snell also admired "its tolerance for those other faiths and its record as a progressive force in the civic life of the town". He attended the Unitarian Sunday School where the teacher, John Kentish-Wright, a local solicitor, introduced him to the work of Thomas Carlyle, Lord Byron and Samuel Taylor Coleridge.
Snell was also a member of the Nottingham Temperance Society where he met John Anderson, a local businessman. Anderson lent him books and helped him find temporary work during long periods of unemployment. Eventually, a contact at the Unitarian Sunday School, obtained work for him as a clerk at the head office of the Midland Institution for the Blind in London.
Living in London gave Snell the opportunity to study. He joined the Mechanics' Institution and used the University College reference library. Books that deeply influenced him at this time included books The Age of Reason by Tom Paine, Progress and Poverty by Henry George and Towards Democracy by Edward Carpenter. Other writers that impressed him included William Morris, John Ruskin and John Stuart Mill.
Snell attended lecturers given by leaders of the National Secular Society in London. This gave him the chance to hear and meet national figures such as Annie Besant, George Holyoake and Edward Aveling. Snell was particularly impressed by Besant who he later described as his "spiritual mother". Besant converted Snell to socialism and as a result of her influence joined the Social Democratic Federation. He was especially impressed with John Burns and helped him in his unsuccessful attempt to become elected as the MP for Nottingham West in the 1885 General Election.
Snell gradually became an orator of some talent and every Sunday morning would speak on the same platform in Beresford Square with H. H. Hyndman, John Burns, Tom Mann, Ben Tillett, Will Thorne, Eleanor Marx, Edward Aveling and Harry Quelch. Snell like the others gave support to the important industrial disputes that took place during that period such as the 1888 Matchgirls Strike and the 1889 London Dockers Strike.
In 1894 Snell joined the Fabian Society. As a result of money made available by the Henry Hutchinson Trust, Snell joined Ramsay MacDonald, Graham Wallas, Catherine Glasier and Bruce Glasier in travelling around the country giving lecturers on subjects such as 'Socialism', 'Trade Unionism', 'Co-operation' and 'Economic History'. Snell was also employed as a lecturer by the British Ethical Union.
Snell was also a early member of the Labour Party and made several attempts to represent the party in the House of Commons. After failing to be elected in Huddersfield in 1910 and 1918 he was eventually elected to represent Woolwich in London in the 1922 General Election.
Ramsay MacDonald granted Snell a title in March 1931 and asked him to serve as Under Secretary of State for India in his government. Although asked to continue in this post when MacDonald formed his National Government six months later, Lord Snell refused. Snell continued in politics and between 1935 and 1940 was leader of the Labour Party in the House of Lords.
Henry Snell died on 21st April 1944.