The War's founder, Ian Bone, and its vocal 'national organiser', Tim Scargill, have started a breakaway group, Class War Organisation (as opposed to the existing Class War Federation). This follows rumblings in the movement about take-over by public-school boys and accusations of irregularity with the finances.
And Mr Scargill will not adorn the Newbury by-election campaign, despite earlier promises that he would 'beat Labour (whom The War dislikes even more than it does Tories) into fourth place'. He did not declare himself as a candidate at Friday's nomination deadline.
Class War kicked off its Newbury campaign two months ago with a leaflet of allegations about the connections and financial dealings of local Conservative party members.
There was also a poster with a photograph of Judith Chaplin, whose death brought about the by-election, and the legend 'One less Tory bastard]'
The divide began at the War's annual conference last year. Mr Scargill attempted to begin Class War's own cultural revolution, and purge the party of 'middle-class theorists'.
'We didn't want the organisation to be a movement for pissed-off rich kids, people who aren't prepared to take to the streets and fight, if need be,' he said. 'So it was a stand-off between those who come from deeply-rooted working-class backgrounds, like myself, and the public-schoolboy types.'
Working-class backgrounds do not come more deeply rooted than Tim Scargill's - he is said to be a relative of Arthur, though he will not confirm this.
But Class War rejected Mr Scargill's move, and he left the organisation with Mr Bone and others.
The breakaway Class War has only 40 members but, according to Mr Scargill, they are the real thing: working-class activists who will return the War to its proper business: 'Mixing it with the cops on the estates and tackling the rich at play.' In the end, Class War's most successful project - its crude but effective newspaper, Class War, which claims 18,000 subscribers - was at the root of the division.
Mr Scargill fulminates against the War's 'middle-class democracy junkies who are only interested in being terribly witty and producing coffee-table reading for the narco-left'.
Class War Federation members were not available for comment, but the Federation issued a statement warning against Messrs Scargill and Bone and their breakaway group. A debate is likely to ensue over who has the rights to the name.
A letter from a Dave Johnson of Class War in an early April issue of Freedom, a rather more sober anarchist newspaper, said Class War members rejected Mr Scargill because money in his charge 'had 'gone missing' '.
Mr Scargill rejected these charges: 'Money missing? What about the pounds 986 they still owe me for a phone bill?'
And he has no real regrets over the split: 'I'll tell you about them: what's really ironic is that their hotline number is a bloody mobile phone]'