She now believes she was 'stupid' and had been hoodwinked by Savile, whom she allowed to sleep overnight at the since-defunct Surrey school. However, in her first interview, she had harsh words for some of her former pupils, who she said had benefited from Savile's visits because he dispensed cigarettes and money.
Referring to the abuse allegations, she said: 'They had an opportunity to tell anybody. But it suited them - some of them, not all of them - to wait 30 years. They're all looking for money ... they come out of the woodwork for money. I do object to my school being targeted .... wild allegations by well-known delinquents.'
Miss Jones described Savile as an 'odd bod' but insisted she had had no idea he was a predatory paedophile.
Since the Savile furore erupted, a string of women have told how he preyed on them as vulnerable underage girls at Duncroft, a state school for 'intelligent, emotionally disturbed' teenagers aged 13 to 16.
Savile would burst into their bedrooms when they were undressing and grope them, and molest them on trips in his Rolls-Royce, they have claimed.
One former pupil, Kathleen Webb - who has now made a statement to police - alleged that when she reported Savile's abuse to the headmistress, Miss Jones replied: 'Don't you dare tell lies like that.' Miss Jones said she does not remember the pupil in question.
Now 91, Miss Jones is living in a Welsh village in the shadow of the Brecon Beacons. She lives independently in a well-kept three-bed semi, cooks her own meals, walks unaided and speaks lucidly and eloquently.
Her neat living room is decorated with framed black and white photographs of her time at Duncroft school, which closed in 1980. She does not remember everything about the events of 40 years ago, but she is crystal clear about what she thinks.
'I was hoodwinked by Jimmy Savile,' she said. 'I thought he was a nice man. Not one person ever told me about Jimmy Savile. Nobody told me he was a pervert. I've just been talking to one of my [former] staff. We are horrified.'
She insisted that if any of her girls had told her what Savile was doing to them, she would have thrown him 'out on his ear' and reported him to police. 'I'm horrified to read some of these girls' statements. I thought, God, why didn't they tell me?', she said.
Savile, who died last October aged 84, groomed the pupils by offering them gifts and tickets to attend shows such as Top Of The Pops and Jim'll Fix It, and then sexually assaulted them in his BBC dressing room.
Toni Townsend, 54, who attended the school in 1972, said: 'Jimmy treated Duncroft like a paedophile sweetshop. He used to take his pick of the mix.'
Another pupil, Carole Wells, 52, said Savile assaulted her in his Rolls-Royce after the headmistress asked if she wanted to go for a ride with him.
Despite claims to the contrary, Miss Jones is adamant the girls never once reported abuse to her. She said: "These girls were getting cigarettes and money from Jimmy. They weren't going to kill the goose that laid the golden egg, were they, by telling me?
"And you didn't go to an approved school unless you were pretty bad. I had to cope with that."
Although the school took girls from difficult backgrounds, she said they were all bright.
"My girls were attractive, intelligent. They could do philosophy, they'd been to good schools," she said. "Air marshals' daughters, surgeons' daughters, teachers' daughters. That's the kind of girls I had."
She added: "Some of the girls were pushing themselves at him [Savile] because of a lack of love and affection in their lives. I'm not criticising them, because they had dreadful childhoods."
Using terms customary for someone born in 1921 and speaking generally, she said: "I know delinquents. They tell you whatever story they feed you. I know these girls. Some of them are lovely; some of them are not. Some of them are so damaged.
"They're not little angels you know. One of the girls had five babies by different men. And I'm not being critical. I'm just saying they were very practised in sex. More than I was.
"They'd have sex with anybody for love. I don't blame them ... he [Savile] was a star. Their life - it was sex. Not that they liked sex, but they could get all sorts of favours in life. Some of them, not many of them, but some of them."
She denies any abuse took place on school grounds, but admits she could not keep tabs on Savile the whole time.
It is also clear from speaking to her that, like so many others in the 1970s, she felt powerless to challenge Savile's status as a national icon who had wormed his way into the affections of figures from Prince Charles and Margaret Thatcher down.
"He was, to me, very odd. I didn't like him," said Miss Jones. "I thought he was an odd bod. But then who am I to judge everybody who came into the school?
"I mean, I met some very strange people in my career. I'm pretty shrewd about men, but I missed out on him, somehow, and I'm annoyed. Because of his background. Because of his OBE, his Royal Family connections and Mrs Thatcher."
She was introduced to Savile in around 1973 by the mother of one of her pupils. "She told me how lovely Jimmy was and how helpful to her daughter. Could he come? I let him come," she says. The DJ would casually turn up unannounced and play records to entertain the girls.
Once or twice, 'Uncle Jimmy' was allowed to sleep over - as were other men including boyfriends of spinster Miss Jones - but strictly in a separate wing from the girls, she said. "I would never leave a girl to be abused."
But why did Savile stay overnight at all? "I forget now. I'm to blame. Because he asked me, probably. He was going to some show or something. I don't know."
A common theme among the stories of abuse is the way Savile lured girls into his Rolls-Royce for rides in the countryside, then molested them.
Miss Jones says she permitted the Rolls-Royce 'treats' on two occasions, and always made sure the girls were in a group. "He said, 'I'll take them for a run'. I had no reason to doubt him. Please remember, my staff were always on the watch. Except when they were off in his car, which I allowed, stupidly."
She added: "Nobody ever complained to me. Not one girl complained to me or my staff. I know they say they did, but they've got to cover themselves, haven't they.
"The school was always open with visitors - magistrates, councillors, MPs - and I encouraged the girls to talk to whoever they wanted to talk to. I never stopped them. So they've no excuse, these girls.
"If they didn't tell me about Jimmy Savile, they deserve all they get. They should've reported him. They knew if they reported him to me I'd report him to the police. And I have reported people to the police."
In 2007, Surrey Police did investigate at least two allegations of abuse by Savile at Duncroft in the 1970s, but the inquiries came to nothing. Miss Jones was not interviewed.
After Savile died, BBC producer Meirion Jones began investigating the school for Newsnight. He is Miss Jones's nephew, and he had visited the school as a teenager where he "could see something odd was going on with Savile", he has told friends. Miss Jones says she and her nephew 'fell out' years ago.
Asked if she felt any guilt about what happened with Savile and her pupils, she said: "No. I did what I thought at the time. And everybody thought the world of Jimmy Savile.
"All the pop stars at the time were having sex with underage girls. However, I don't think he had proper sex because he didn't have time. I think he mauled them and pawed them, which I didn't notice.
"He pawed me, but I thought he was an eccentric. My mother couldn't stand him. But I put up with it because the girls loved Jimmy Savile. Stupid me. I must say he was very clever. I thought I was clever but he was cleverer."
- Daily Mail