This Wikipedia entry on Soviet anti-Zionism is very illuminating if you are trying to understand the Corbyn/Livingston master narrative en.wikipedia.org/wiki/Soviet_an…
Essentially, the Soviet Union initially supported Zionism in the 40s because many of the early Zionists were strongly socialist (see the Kibbutz movement). The USSR was the second country to recognise the Jewish state in 1948. But everything changed after that... 
As Israel because closer to the USA, especially after 1967 Six Day War, the USSR switched its view on Zionism and reverted to a Tsarist world Jewish conspiracy view. Note how this language reflects Corbyn's (and so many of the more extreme comments I receive from his supporters)
And look here, it's Ken Livingstone's theory about Hitler and Zionism - all part of the master theory
This was all going on really up to the end of the Soviet Union, but appears to have been kept alive in certain corners of the political left
I recommend people read @DAaronovitch's latest book for a sophisticated and illuminating understanding of British communism, from the perspective of someone who grew up in it. It's basically the prequel to Corbyn's Labour and covers many of these points amazon.co.uk/Party-Animals-…
