Ken Livingstone has clashed with the Jewish community [read Zionist movement] many times since the 1980s, when he was the leader of the Greater London Council.
In 1981, as co-editor of the Labour Herald newspaper, he ran a cartoon entitled "The Final Solution", depicting the then Israeli Premier, Menachem Begin, as a Nazi [as did Albert Einstein and Hannah Arrendt in 1948]. He is seen in SS uniform, giving the Nazi salute and standing on a pile of dead bodies, saying "Shalom? Who needs shalom with Reagan behind you?".
During a 1984 interview with Israeli newspaper Davar Hashavuah, he claimed the Board of Deputies had come under the control of "reactionaries and neo-Fascists." [in a word: Zionists]
In October 2002, he denounced Ariel Sharon as "a very unstable leader with a record of war crimes and mass murder."[ not a miilion miles from findings by the Israeli Supreme Court]
Last year he welcomed to London Muslim cleric Sheikh Yusuf al-Qaradawi, who has endorsed Palestinian suicide bombings and is accused [in common with Orthodox Judaism] of backing the killing of gays and the beating of women. When a cross-communal [which communities?] coalition, including the Board of Deputies, asked to meet him to discuss their concerns he refused. He argued their claims were lies peddled by a "Zionist front organisation." [MEMRI: a Zionist front organisation]
At a GLA meeting last month, he was amused at the prospect of a stormy meeting with the Board of Deputies over his condemnation of Israel, joking: "They should have sold tickets for that one."
So, not one thing that could be described as anti-Semitic. Obviously his hostility to Zionism is going to annoy some Jews, but by no means all. But it looks like he's starting to wobble so perhaps the Zionists will win this round after all.