One senior Labour Party figure told the JC: "Jack's actions speak for themselves.
"He has been the first one to blame the alleged Israel lobby for Labour's defeats under Jeremy Corbyn.
"But he is the one disloyal enough to campaign against Labour at a general election."
Mr Thomas was first exposed by the JC in July 2018 after he spoke at a Momentum meeting featuring Mr Williamson in Liverpool.
In a speech, Mr Thomas told the left-wing gathering: “What could be a greater threat to our democracy than a foreign government who [sic] is trying to veto the person we want for Prime Minister?
"Of course, I'm talking about the Israelis with their footsoldiers in Labour - the LFI, the JLM. They are trying to take our democracy away from us."
On Monday night at a Labour rally for leadership candidate Rebecca Long Bailey, Mr Thomas was filmed saying: "The people who prevented Jeremy Corbyn becoming Prime Minister most are Tom Watson, John Mann and Margaret Hodge and they are all members of the Israeli lobby - why on earth did you declare yourself to be a Zionist?"
The JC has contacted Labour for comment on Mr Thomas and his conduct ahead of publication of this article.