The actor, who joins Coronation Street next week as Ken Barlow's long-lost son, added that fans approach his father everywhere he goes.
Speaking to the Sunday Mirror, he said: "We went for a walk together the other day and these young girls were saying, 'Oh, we love Bill Roache, we've always had a thing for him'. And they weren't joking, it was for real.
"Dad is an inspiration to me. I don't like talking about his age, but he's 78, which is unbelievable and I literally cannot relate to him like that. He's full of vitality and extremely healthy. He's a sex symbol, for God's sake.
"I hardly ever get recognised in this country, it's just my dad - and it even happens in New York. We went to the top of the Empire State Building and someone went, 'Ooh, look, it's Ken Barlow over there'. It was worse when I was younger.
"I remember once he was judging a beauty contest on the Isle of Man in a big open-air swimming pool that had been emptied out. There were literally thousands of people there and as we arrived and got out of the car, suddenly hordes of people swarmed forward trying to get through the barricades screaming, 'Bill! Bill!' I was seven years old and holding his hand, and I remember thinking it was like he was one of The Beatles."