Mr Corbyn said the programme adopted a "pre-determined position" before it was aired earlier this week.
"Our party members do have the right to be heard if they're accused of anything and our party staff have a right to be supported and they are supported."
The Labour leader said he will fully cooperate with the EHRC.
"Anti-Semitism is a poison, it is vile, it is wrong," he said. "It is a poison in our society and any other society."
He added: "It is not acceptable in any form."
Mr Corbyn said anyone in the party who commits any act of anti-Semitism faces withdrawal of membership or expulsion and "that we have done".
He said: "We investigate every case that comes up.
"It's less than 0.1% of our membership that have ever been involved in any accusation, never mind any resolution of the issue."
He said: "We are processing them in a timely manner and I believe that anyone looking at our process will say actually this is a robust process and maybe we'll invite other political parties to adopt the same diligence that we have adopted."
Ms Formby, Labour's general secretary, has been criticised since the Panorama documentary and Mr McCluskey said this would be wrong in normal circumstances - but is even worse given that she is fighting cancer.
He told thousands gathered in the rain on Durham Racecourse: "I have a simple message for Tom Watson and his pals in the media - a simple message to Tom and his pals: You should f****** well be ashamed of yourselves.
"Jennie, our message to you is that the Durham Miners' Gala stands with you."