The Labour Party announced her resignation before the Channel 4 interview was broadcast. Lady Turner agreed "it would be inappropriate" to stay on the front bench.
Questioned about Mr Greer's decision to abandon his libel case against the Guardian, she said: "It is always a lottery to enter into litigation but I did firmly believe, and I still firmly believe, in the innocence of Ian Greer and I will continue to support him while I believe that."
She saw no reason why she should not be on the front bench while being a director of Ian Greer Associates, one of the most prominent parliamentary lobbying groups.
Lady Turner said Mr Greer was "absolutely in the clear. I have no intention of resigning because to do so would look as though I believed something in the allegations and I don't. I am quite certain Ian has behaved completely honourably throughout. My position is absolutely clear: while I continue to believe in his innocence I shall continue to support him and I shall continue to remain a member [of his business]."
She defended Mr Greer's payment of pounds 10,000 to Neil Hamilton for business introductions the Tory MP made. "It is quite a standard commercial practice to pay commission to people who introduce business to you," she said.
Asked if she thought she should remain on the front bench, Lady Turner said she saw no reason why she should not.
The leadership apparently did not agree. Within hours, Lord Richard, Labour leader in the Lords, issued a statement announcing her resignation. "There is no suggestion that she has acted improperly in her capacity as a director of his company," he said.
Gordon Brown, the shadow Chancellor, said there had been a conflict of interest.
Mr Hamilton should now resign as an MP, he said. "I don't think there is any place in public life for what he did. There are two facts that are absolutely clear - Mr Hamilton did receive pounds 10,000 at least for services rendered and he misled Michael Heseltine when he was asked about it . . .
"Mr Major should condemn his behaviour and say to him he should not be a Conservative candidate at the next election."Reuse content