Robinson, now 49, told ITV1's This Morning that the first assault took place when she was 12 years old.
"He called me over to sit on his knee, but I was sat in the middle, I was literally sat on the groin part of him. He talked to me and he'd lower the tone of his voice, so the more quiet he got the more I had to lean in to hear him," Robinson recalled.
"Then I thought, 'There's something wrong here'. He was stroking my back, caressing up and down my spine, and it didn't feel right. It felt weird, but he decided to carry on.
"Because I had a short skirt on and didn't want to spoil my best dress I lifted my skirt up so I was sat on him with just my knickers. The more he rubbed his hand up and down my back and went closer towards my pants, I thought, 'Something's hard here.
"Something's uncomfortable, what am I sat on? Car keys?' So the more I wiggled, the more excited Jimmy got. The next minute I know, his hand is on my bum, he'd gone into my knickers. This was in a room full of people. Nobody saw - he got it down to perfection."
Robinson told her grandmother - Savile's older sister - who was sat opposite at the time. She told her, "It's only Jimmy, don't worry, I'll sort it out," but no further action was taken.
Asked if she believes Savile bought his sister's silence, Robinson replied: "Of course I do. Anything she wanted, she got. From holidays that she wanted, she got a cottage, she stayed in a Bupa sheltered home."
Another incident occurred when Savile was the DJ at Robinson's engagement party. "He touched my breasts," she continued. "He tried to fondle. He wanted me to touch his willy, and I didn't want to.
"I told him to get off, that I didn't like it, but the music was that loud and the people were talking that no matter how much I tried to shout, nobody heard. So I thought if I could just go along with it, the sooner I did what he wanted me to do the sooner it'd be over.
Robinson added: "[My family] are not happy. My mum supports me, but the family, no. I think it was [a shock] to her because mums try to protect your children and she feels guilty that she wasn't there to protect me.
"If we blabbed on Jimmy or told tales, the fame that surrounded him would've gone. And I loved to say that Jimmy Savile is my uncle - I loved to say it, it made me proud. But for him to suddenly be destroyed over something like this, the family would have had nothing.
"It's scary. It's making somebody listen and believe you. I would've kept the secret until I died, because its family, but looking back at all these other victims of his abuse, it was like a mirror image of what happened with me."
It was recently announced that the Metropolitan Police enquiry into alleged sexual abuse of children by Jimmy Savile and others has now become a formal criminal investigation.