The son of a rich businessman, Hyndman was born in London. After being educated at home, he entered Trinity College, Cambridge. After achieving his degree in 1861 he studied law for two years before deciding to become a journalist.
In 1866 Hyndman reported on the Italian war with Austria for the Pall Mall Gazette. Hyndman was horrified by the reality of war and became violently ill after visiting the front line. Hyndman met the leaders of the Italian nationalist movement and was generally sympathetic to their cause.
In 1869 Hyndman toured the world visiting the United States, Australia and several European countries. He continued to write for the Pall Mall Gazette, where he praised the merits of British imperialism and criticised those advocating Home Rule for Ireland. Hyndman was also very hostile to the experiments in democracy that were taking place in America.
Hyndman decided on a career in politics but, unable to find a party that he could fully support, decided to stand as an Independent for the constituency of Marylebone in the 1880 General Election. Denounced as a Tory by William Gladstone, Hyndman got very little support from the electorate and, facing certain defeat, withdrew from the contest.
Soon after the election Hyndman read a novel based on the life of Ferdinand Lassalle. Hyndman became fascinated with Lassalle and decided to research this romantic hero who had been killed in a duel in 1864. Hyndman discovered that Lassalle had been a wealthy socialist who had financially supported the work of Karl Marx. Hyndman decided to read The Communist Manifesto and although he had doubts about some of Marx's ideas, for example, the inevitability of a socialist revolution, he was greatly impressed by his analysis of capitalism.
Hyndman then decided to form Britain's first socialist political party. The Social Democratic Federation (SDF) had its first meeting on June 7, 1881. Many socialists were concerned that in the past Hyndman had been opposed to socialist ideas, but Hyndman persuaded many that he had genuinely changed his views, and those who eventually joined the SDF included William Morris, George Lansbury and Karl Marx's daughter, Eleanor Marx. However, Friedrich Engels, Marx's long-term collaborator, refused to support Hyndman's venture.
To publicize the SDF, Hyndman wrote a book in 1881, England for All, where he attempted to explain the ideas of Karl Marx. This was followed in 1883 by Socialism Made Plain, where he provided details of the policies of the SDF. This included a demand for universal suffrage and the nationalization of the means of production and distribution. The SDF also published Justice, edited by the talented journalist, Henry Hyde Champion.
Although Hyndman was a talented writer and public speaker, many members of the SDF questioned his leadership qualities. Hyndman was extremely authoritarian and tried to restrict internal debate about party policy. At a SDF meeting on December 27, 1884, the executive voted by a majority of two (10-8), that it had no confidence in Hyndman. When Hyndman refused to resign, some members, including William Morris and Eleanor Marx, left the party.
In the 1885 General Election, Hyndman and Henry Hyde Champion, without consulting their colleagues, accepted £340 from the Tories to run parliamentary candidates in Hampstead and Kensington, the objective being to split the Liberal vote and therefore enabling the Conservative candidate to win. This strategy did not work and the two SDF's candidates only won 59 votes between them. The story leaked out and the political reputation of both men suffered from the idea that they were willing to accept "Tory Gold".
Hyndman continued to lead the SDF, and took part in negotiations to establish the Labour Representation Committee in 1900. However, he left the SDF when it became clear that it was deviating from the objectives he had set out and in 1911 he set up the British Socialist Party (BSP).
Hyndman was critical of moves by James Connolly and John Maclean to set up socialist parties in Ireland and Scotland respectively, arguing instead that they should stay within his mainstream British socialist movement.
Hyndman upset members of the BSP by supporting Britain's involvement in World War I. The party split in two with Hyndman forming a new National Socialist Party. Hyndman remained leader of this party until his death.