The SDF was an outwardly Marxist party but contained many members who, whilst being socialists, did not consider themselves Marxist. They took part in many elections but met with no success.
On November 13, 1887, the SDF organised and participated in the demonstration in Trafalgar Square that resulted in what became known as Bloody Sunday. Friedrich Engels severely criticised Hyndman for encouraging workers to take part in riots that he hoped would lead to revolution. Engels believed that British workers were not yet intellectually ready to take part in the uprising that would overthrow capitalism.
In 1890 the SDF was involved in internal conflict. Some members such as John Burns and Tom Mann believed that the SDF should be more active in trade union activities. Hyndman disagreed, as he wanted to concentrate on the main objective, bringing about a socialist revolution. Although outnumbered, Hyndman refused to change the strategy of the Social Democratic Federation, and Burns and Mann left the party.
They were later followed by others such as Henry Hyde Champion, Ben Tillett, Philip Snowden, and George Lansbury, who joined the Independent Labour Party (ILP), which was led by James Keir Hardie, who proposed a Christian Socialism, rather than the atheistic Marxism of the SDF. The ILP also had the advantage of having Hardie as a member of the House of Commons after winning the West Ham South seat in the 1892 General Election.
On February 27, 1900, Hyndman and the SDF met with the ILP, the Fabian Society and trade union leaders at the Memorial Hall in Farringdon Street, London. After a debate the 129 delegates decided to pass Hardie's motion to establish "a distinct Labour group in Parliament, who shall have their own whips, and agree upon their policy, which must embrace a readiness to cooperate with any party which for the time being may be engaged in promoting legislation in the direct interests of labour." To make this possible the Conference established a Labour Representation Committee (LRC). This committee included two members from the Social Democratic Federation and the Independent Labour Party, one member of the Fabian Society, and seven trade unionists.
The LRC eventually evolved into the Labour Party. Many members of the party were uncomfortable with the Marxism of the SDF and Hyndman had very little influence over the development of this political group. Hyndman eventually left the Labour Party. In 1907, he renamed the group the Social Democratic Party, and in 1911 established a new group, the British Socialist Party (BSP).
The Social Democratic Federation was also the name of a party led by Hyndman after 1919, when the National Socialist Party changed its name. The group enjoyed some short-term success but gradually faded into the Labour Party.
There was also a Social Democratic Federation in the United States. It was formed in 1936 by a group of anti-Trotskyists in the Socialist Party of America. They supported Democratic Party and Liberal Party candidates, but as the Socialist Party moved to the right, the SDF felt able to rejoin it, and did so in 1956 (with the exception of a small group which formed the Democratic Socialist Federation).