I was looking for these dates which I found in a comment thread and am posting them here for future reference. If I ever have time, I will evidence all this with links.
April 2005: Atzmon rave review in Socialist Review by Brian Richardson, announcing forthcoming gig at Marxism event.
Summer 2005: The SWP's Socialist Review has a rave review of Atzmon's Orient House ensemble tour (only note of criticism is that he likes Ken Livingstone too much), and Atzmon plays Marxism 2005 as well as speaking at Bookmarks. Jews Against Zionism picket the Bookmarks event. JAZ are not by any means an oversensitive pro-Israel group, but made up of left-wing people like Tony Greenstein, Moshe Machover and Hilary Rose. Leading left-wing anti-Zionist website Labournet plays major role in this. SWP responds with a statement that refuses to accept any truth in the allegations.
2006: SWP organises “Five for Trane” concerts featuring Atzmon and the SWP's Martin Smith. At least six gigs (March, June, October, etc, etc).
Autumn 2006: Atzmon speaks and plays alongside George Galloway (then in alliance with the SWP in Respect) and Martin Smith at an SWP-organised Stop the War event in Tower Hamlets. (The SWP boasted it was a successful fund-raiser for them, and Smith interviewed Atzmon for Socialist Worker. Atzmon told Smith "I will be playing at the Cultures of Resistance concert because I support the Socialist Worker appeal... “For me to play jazz is to fight the BOB (Bush, Olmert and Blair) world order.")
January 2007: Michael Rosen, a high profile Jewish anti-Zionist very close to the SWP, criticises SWP for hosting Atzmon. Organisers of the SWP's Cultures of Resistance (Hannah Dee, a current SWP CC member, and Viv Smith, a former CC member) deny he is an antisemite (archived). Evidence? “We would never give a platform to a racist or fascist. Our entire history has been one of fierce opposition to fascist organisations and antisemitism.” Therefore impossible that Atzmon could be a racist, because he was invited to our event.
Summer 2007: Atzmon plays Cultures of Resistance gig at Marxism 2007, and reprises the Martin Smith collaboration in Liverpool, and later Pete Segal in Socialist Review gives another rave review of his CD Refuge, with no note of criticism or mention of Rosen's letter.
Autumn/Winter 2007: Atzmon plays an SWP fund-raiser, Now’s the Timer, with Martin Smith. Four gigs. Positive reviews ("Politics continues to drive Atzmon’s music forward") of his records in Socialist Worker. Martin Smith also mentions him in another Socialist Review article.
January 2008: Atzmon now an explicit Holocaust denier, as revealed by Tony Greenstein and others, eliciting no comment from the SWP, despite their close association with him.
May 2008: Socialist Review again promotes Atzmon, listing him in their “Five things to get or see this month”
April 2009: Another Socialist Review rave review of an Atzmon CD, In Loving Memory Of America, again no note of criticism.
October 2010: SWP promotes the Jazza Festival, featuring Atzmon and several Atzmon-linked groups.
November 2010: No trace left on any SWP website of their earlier statements and clarifications about Atzmon.