Sir Michael Parkinson was diagnosed with prostate cancer in May after a routine health check and doctors immediately began organising his treatment, which involves five sessions of radiotherapy a week.
The renowned journalist and interviewer said he was left in shock by the diagnosis, but said he was "in wonder" at the "marvelous" work of medical staff after initial thoughts of his own mortality.
The 78-year-old said: "I had to start calling a few of my social engagements to tell them I couldn't do it - what do you say to them?
"When you are told you have something like cancer, it is a shock. But the cancer specialist said: 'I will assure you, you will not die of this.'
"I am concerned about it, of course, but I am not frightened of it."
Michael Parkinson, speaking in an interview to be broadcast tomorrow night on Classic FM, said he "didn't much like" Jimmy Savile and "couldn't understand why he became so popular."
He went on defend the BBC on one aspect of the criticism levelled at the corporation:
But I'll make one observation about the BBC. The BBC got a kicking on that. But at least he had a reason for being at the BBC. He was employed by the BBC and he had to work there.
What on earth was he doing, what was his reason to be at Broadmoor? What was his reason to be at Stoke Mandeville? What was his reason to be at the hospital in Leeds and, particularly, what reason did he have to go to a school?
Come on. That's the worst aspect of it, I think. At least at the BBC he had to be there, he was employed by the BBC.
Parkinson said he first met Savile in Manchester in the 1960s when they both worked at Granada, adding:
But he was not a man who sought the company of people, with hindsight now, who couldn't help him. In those days, we didn't know he was being selective, we just thought he got his own gig and off he went to do it. Nobody ever got really close to him at all.