Most Rev Justin Welby has insisted he was "completely unaware" of the allegations after the Church issued an apology over its handling of the claims.
The accusations relate to John Smyth, a former leader at the Iwerne camp, which had close links with the Church of England and where Justin Welby worked as a dormitory officer in the late 1970s.
Claims against Smyth were uncovered by Channel 4 News. He is a prominent QC and part-time judge, now based in South Africa.
"I'm not talking about that," he said when approached by the broadcaster.
The Iwerne Trust, which oversaw the Christian camps, was made aware of the allegations and compiled a report in 1982 but failed to tell police, Channel 4 News said.
Archbishop Justin said he was "completely unaware" of any allegations when he worked at the camp.
He said on LBC Radio: "I was at that particular camp in the mid-70s. I was young then - 19 to 21 or 22.
"I never heard anything at all, at any point."
Speaking about Mr Smyth, the Archbishop added: "I wasn't a close friend of his. I wasn't in his inner circle or in the inner circle of the leadership of the camp, far from it."
He said he was first told about the alleged abuse in late 2013 or early 2014 and that by that point it had been reported to the police.
"I have a vague feeling I may have had a Christmas card in the 1990s and when I was living in Paris he passed through and I shook hands with him, that was the limit," he said of his contact with Mr Smyth since.
Lambeth Palace said in a statement that "although the Archbishop worked with [Smyth], he was not part of the inner circle of friends; no-one discussed allegations of abuse... with him."
It went on: "We recognise that many institutions failed catastrophically but the Church is meant to hold itself to a far, far higher standard and we have failed terribly.
"For that the Archbishop apologises unequivocally and unreservedly to all survivors."
Speaking on Premier's News Hour Justin Humphreys, from the Churches Child Protection Advisory Service said Archbishop Justin's apology was "a positive thing".
But he added: "Unfortunately this yet again does give the public at large a very poor view that these sorts of things are taking place".