He says: "I don't want anything from my dad, just his recognition.
"Not having a father growing up was tough. All I ever wanted was his love. People think I look and sound like a younger version of my dad.
"I sing all his songs. People stop and stare as soon as I start singing."
Jon was born after the Welsh superstar enjoyed a three-day fling with Katherine Berkery, then a 24-year-old model, in New York in October 1987.
Sir Tom denied he was Jon's father until it was proved by a court-ordered paternity test in 1989, and the singer agreed to pay £1,700 a month maintenance for his upkeep until his 18th birthday.
Jon says: "There was never a birthday card, a single Christmas card, a call. I grew up with images of dad all around. But my calls and emails have gone unreturned. He wants nothing to do with me."
Sir Tom only acknowledged Jon's existence in 2008, saying: "It wasn't something I planned. I was tricked. I fell for the seduction."
It was a cruel blow for Jon, who says: "Those words hurt. It wasn't my choice to be born. You don't get to be as famous as my father without being prepared to hurt people along the way."
Jon says his father's rejection led to an angry drink-and-drug-fuelled teenage rebellion and meant he 'couldn't form proper relationships with girls'.
Jon has even considered confronting his dad at one of his concerts or even auditioning for ITV talent show The Voice, where Sir Tom is a mentor.
The irony of his father offering advice to others is not lost on his son, who says: 'All I want is the chance to sit down with him. I truly don't want anything from him.'
A video of Jon's busking can be viewed at MailOnline.