Complex sentence: He was a member of the Labour Party from the 1980s until 2001, when he joined the Liberal Democrats, remaining with them until 2003, when he remained a political independent for some time before defecting to Veritas.
Split into simpler sentences: He was a member of the Labour Party from the 1980s until 2001. The following year he joined the Liberal Democrats, remaining with them until 2003; he then remained a political independent for some time before defecting to Veritas.