I believe he is and you're right, anti-Zionism isn't the same as anti-Semitism but the word 'Zio' is something altogether different and intended to be offensive.
Greenstein has been suspended for alleged anti-Semitism and says there's a witch-hunt against him but his Twitter account is littered with the word "Zio". Shami Chakrabarti's report referred to that word as “a term of abuse, pure and simple, and should not in my view have any place in the...
Tony Greenstein has quite a bit of history with Lord Bassam, they're certainly not besties. This is from Greenstein's blog last year.
http://azvsas.blogspot.co.uk/2016/09/the-noble-sayings-of-lord-bassam-masque.html