When he was 19, Frank Sinatra Jr was kidnapped and held to ransom for four days. This would be a terrible thing to befall any son of rich and famous parents, but all the more so somehow for someone who had spent his adolescence trying to remain invisible. "I never felt that it was in anyone's best interest to be looked at differently by other people because of a name," he says. "I kept to myself a lot."
But when the father he rarely saw paid the ransom – reported to be close to $240,000 (£1.3m in today's money) – Frank Jr became headline news around the world. The timing was bad. He had just recently launched himself as a singer and musician, which he hoped would establish him in his own right. Now such hopes were scotched.
The real damage, he suggests, was not the kidnapping but what happened afterwards. "The criminals invented a story that the whole thing was phoney." It wasn't, and they duly went to prison, but the rumour that it had been a publicity stunt staged by his father to help his son's fledgling career stuck.
"That was the stigma put on me," he says. In a way, he has lived with it ever since.
Nancy Sinatra's younger brother, Frank Jr was born in 1944. By the time Frank Jr was six, his father had split from their mother and it would be another four decades before they had anything like a proper relationship.
"He was a good father as much as it was within his power," is how he puts it, diplomatically. Frank Sr, he explains, was making two films and four albums a year in the 50s and 60s, and touring incessantly. Frank Jr saw more of him on the big screen than he did in the flesh, and considered being the man's namesake a heavy burden.
Frank Jr likes to say that in an ideal world he would have excelled at school and gone on to run General Motors. But he didn't, and so he couldn't. He was a gifted piano player, though, and by the age of 18 realised he could sing too. Not only was there a disarming family resemblance, but he had the same dark, chocolatey voice. Comparisons were inevitable, exacerbated by his decision to make much the same sort of music and play the same casino circuit.
"At first I felt like I was living in his shadow," he agrees, "but I did develop my own following eventually, so I must have been doing something right."
There were intermittent television appearances over the years – often as a guest on the shows of his father's Rat Pack cohorts, Dean Martin and Sammy Davis Jr – but only the occasional album. Instead, touring was his thing, and he played in 81 countries across the world.
That he never strove to compete with his father suggests he found it impossible, and so didn't bother to try. But presumably his long career has been a fulfilling one?
"Yes, but does it really constitute actual success?" he muses. "Over all these years, I have never had a hit movie, never had a hit television programme and never had a hit record. To my way of thinking, that means success has not been achieved. I have made no mark of my own creation. This," he concludes, "is something to be considered."
Interviewing a 68-year-old Frank Sinatra Jr is, you cannot help but feel, a markedly different experience to what it must have been like when he was 28 or 38. He has found the kind of peace that likely eluded him for much of his professional life. On this summer afternoon, he is charming and erudite company, full of candour and unerringly calm.
"My lack of success does not trouble me at this stage in my life, no," he says. "When I was younger, sure, I wanted to have some degree of, shall we say, identity. But it never came."
Even after Frank Jr's kidnapping ordeal, his father failed to become much of a tangible presence in his life. Frank Sr, it seems, was too busy. There were more films, more albums, more women to marry. They would, Frank Jr says, meet on occasion and talk on the phone, but rarely more than that. It wasn't until he was 44 that his father finally invited him into the inner circle.
"It was 1988 and I was in Atlantic City getting ready to do one of my shows," he begins, "when Sinatra came on the line and told me he wanted me to conduct his band for him."
He pauses with all the timing of a light entertainer.
"Well, after my friends had revived me with the smelling salts, I said to him, 'You can't be serious?'"
Sinatra was. Frank Jr took the job, and spent the last seven years of his father's career touring with him. The US public were fascinated (and nosy), which meant Frank Jr became adept at avoiding giving answers to questions that probed too deeply into the private life of one of their biggest stars. He pleaded mitigating circumstances: when at last father and son did bond, his father was an old man, a shadow of his former self.
"When I came on board, Sinatra was already 72. He was slowing down."
In private moments, he says, he often found him withdrawn. "I would see him very up, then very down, and sometimes very sad. It often came to it that I simply held him, just held on to him and told him I was here for him. I owed him that. "And in that church on that afternoon in 1998, when I was looking down at his casket covered in flowers, I was grateful that at least he hadn't died with us as strangers, that I had been able to get to know him, and he had been able to get to know his son."
According to various online sources, Frank Jr has two sons himself, Frank Sinatra III, born in 1978, and Michael, a decade later. The former made the news two years ago after a reported suicide attempt. When I ask about that, he says, "No, I have one son, and his name is Michael."
And of the reports to the contrary? "There are certain people who make all sorts of claims," is all he says.
About Michael he is happy to talk. "He is 25 now, almost 26. He lives in Japan, a college professor. He gets back to the United States probably once a year and I make damn well sure that we stay in contact. Whenever he does visit, we go to dinner, just the two of us. I want him to have what I didn't."
Frank Jr, who is no longer married, arrives in London this month with his band. His show is called, perhaps inevitably, Sinatra Sings Sinatra.
"Well, that's what some people want to call it, but I've never felt particularly comfortable with that," he says. "The way I see it, before I can sell an audience Frank Sr, I have to sell them Frank Jr first. Sinatra is a very established commodity over here, whereas I …"
He smiles again and trails off, the fires that doubtless once raged in his youth now merely smouldering embers.
"If the audience comes, and likes what I do, then that's enough for me," he says. "I'll settle for that."