It was founded in the early 1980s in a split from London and Scottish branches of the Socialist Workers Party, of which, for many years, it considered itself an "external faction".
The RDG believed that the far left concentrates excessively on economic struggles without a clear focus on the need for democracy.
For the 1987 general election the RDG joined the Red Front, an electoral alliance spearheaded by the Revolutionary Communist Party.
In the late 1990s it joined Arthur Scargill's Socialist Labour Party, officially dissolving and becoming the Republican Group.
The RDG had patchy relations with the Communist Party of Great Britain (PCC) and occasionally had articles in that group's paper, the Weekly Worker.