In the second programme of this series, Matthew Parris meets the Revolutionaries: The Revolutionary Communist Party of Britain (Marxist Leninist) doesn't have many members but has all the features of an elaborate organisation.
It has a Central Committee, it holds Party Congresses, it has Party Cadres and it produces pamphlets and a newspaper.
Its leader, Chris Coleman, is no wild eyed hothead, but a self-effacing elderly man in a suit.
He's a supporter of North Korea.
He's convinced the revolution will happen here, but admits he's not quite sure when.
Rob Griffiths, General Secretary of the Communist Party, isn't making any predictions either.
He's hoping the Communists will eventually play a part in some sort of broad left wing coalition government.
The Communists think big - they want to see an end to American world dominance and to that end they're out campaigning hard in shopping centres round the country.
Dave Nellist of the Socialist Party was once a Labour MP in Coventry but was thrown out of the party for being too left wing.
But he had a big local following and nothing daunted, won a seat on the Council.
There are now three Socialist Councillors in the City.
Dave Nellist thinks things are moving the Socialist way.
He thinks that if conditions are right and if he can get some of the big unions on board, there could be a "breakthrough" in the next two to five years.