Campbell also told the inquiry about his objective to 'neutralise' the Sun newspaper
During his appearance before the inquiry Campbell spoke about his objective to "neutralise" the Sun newspaper to "try to ensure we had a more level playing field where we could communicate to the public what we were trying to do".
But while this was his objective he did not predict the Sun's decision to back Labour in 1997.
Campbell said looking at the period of 1995 to 1997, the Sun was a "significant player in the media marketplace" and Rupert Murdoch was the "single most important media figure". He said it was part of his job "to help Tony Blair communicate to the public and part of that was through the media".
He added: "The Labour party for some years had nothing to do with Murdoch papers whatsoever, we made an active choice to change that approach."
But he said he was never "witness to and don't believe there was ever a discussion of ... 'Tony if you do this my papers will back you'.
"It just never happened. I believe Blair went through these issues on their merits."
He added there were "lots of areas you'd be hard-pressed to say the Murdochs were getting good business out of the Labour government".
Campbell was asked about an article in the Sun in 1997 by Blair on his commitment to a referendum before entry to the Euro.
Campbell said they knew what was wanted "rhetoric wise" but that this did not involve a change in policy.
He told the inquiry "it was made clear by the editor" that if Blair emphasised his commitment to a referendum, this was "likely to be the final piece of the jigsaw".
But this policy was "already set", Campbell added.
"I don't think on policy anything was ever traded with Murdoch or any other media owner."
Later in his evidence Campbell was also asked by Lord Justice Leveson if he felt there was an appetite to address the cultural issues being highlighted by the inquiry, today, to which Campbell replied: "No, if I'm being frank".
"I don't think there is much of an appetite. I think there is some appetite for a cross-party approach but I wouldn't rule out the possibility of politicians looking to see how this might affect their positioning vis-a-vis the next election. There is some appetite for change but I wouldn't overstate it."