Sir Richard Dearlove said the Labour leader had associated himself with people who were not “friends of the British nation”.
Appearing on Sky News’ Sophy Ridge on Sunday programme, Sir Richard said: “Someone coming from my background is troubled by Jeremy Corbyn’s past associations, some of which I find surprising and worrying.
“He may have abandoned them now but I don’t think he can entirely, as it were, dump your past.
“He’s enthusiastically associated himself with groups and interests which I would not say were the friends of the British nation.”
Sir Richard also dismissed the idea of a “deep state” working against the Labour Party, saying: “It’s rubbish. I think every government has been loyally served by the British security and intelligence community.”
Shadow chancellor John McDonnell dismissed Sir Richard’s comments, describing him as “a reactionary member of the establishment”.
Mr McDonnell said: “Well, I’m not surprised. Look, this is a member, a reactionary member, of the establishment, so I don’t think he’d welcome a Labour government of any sort, to be frank.
“Can I just say to him directly, I think he should spend his retirement in quiet contemplation of the role that he played with regard to the Iraq war where over half a million people at least were killed. He was strongly criticised as the head of an organisation whose intelligence took us into that war so I think he should have a bit of humility about the judgments he makes about individuals and others in the future.”
Mr McDonnell also accused Theresa May of hypocrisy after the Prime Minister condemned personalised attacks on Diane Abbott.
He dismissed speeches at the Tory party conference criticising the level of abuse against Ms Abbott as he accused the Conservatives of “setting the dogs” on the shadow home secretary during last year’s general election.
He said: “I find it a bit hypocritical that [Home Secretary] Sajid Javid and the Prime Minister referred to Diane in that way because it was the Conservative campaign, the Conservative Party campaign, that during the election said a lot of the criticism, well, that set the dogs on to Diane.
“If you look at what happened in the media, the Tory press were abysmal and that was set up by the Conservative Party during their campaign. They personalised the campaign because they did not want to debate the policy issues.”
The shadow chancellor said Labour would scrap universal credit.
Until now, the party’s policy had been that it would pause the controversial welfare reform and make changes to the system.
Mr McDonnell said: “I think we are moving to a position now where it is just not sustainable. It will have to go.”