But more than that, Jared also seems to have inherited Richard's stage presence. He has the innate capacity to grab your attention without even speaking, a trait he puts to good use in his latest role as the wily Captain Anderson in BBC2's epic new three-part adaptation of William Golding's seafaring trilogy To the Ends of the Earth.
Anderson is commanding a ship undertaking an immense, and immensely perilous, nine-month voyage from England to Australia in the early 19th century. The trip is told through the eyes of an unworldly aristocrat, Edmund Talbot (played by Benedict Cumberbatch). Much of the work echoes the themes of Golding's celebrated The Lord of the Flies. Homing in on a febrile, enclosed community,To the Ends of the Earth underlines Golding's view that "man produces evil as a bee produces honey".
Lying on the grass in a west-London park on a summer evening, Harris observes that To the Ends of the Earth gives a gritty, warts-and-all depiction of the true horror of such a journey. "The director, David Attwood, wanted the drama to be an accurate representation of what it was like to pull off a trip on the sea in those days. By the end of the series, the ship is on its last legs; it is leaking, about to be decommissioned, and it is doubtful that it will even complete the voyage.
"Above all, David was eager to deglamorise the idea of the beautiful high seas. He wanted to make To the Ends of the Earth as frightening as it must have been. Even today, with all our technology and safety features and rescue teams, the most dangerous jobs in the world are at sea. So, back then, it was lethal. Everyone was taking a huge risk just by setting foot on a boat."
In the course of their often hugely dangerous journey, Anderson and Talbot engage in a high-stakes power game. The captain's very first words in the drama are a booming rebuke to Talbot, who has broken the ship's rules by stepping uninvited on to the quarter-deck. "Who the devil is this?" shouts Anderson. "By Christ, am I to be outfaced on my own deck by every ignorant bastard?"
The actor is quick to emphasise: "Personally, I'm not at all like Anderson. In fact, the only thing I ever captained in my life was my football team - and that was on my birthday!"
Harris brings to the role the same grizzled-mariner charisma that his father invested in the role of Seaman John Mills in the 1962 version of Mutiny on the Bounty. A characteristic that the son does not share with the father, however, is Richard's reputation as a hell-raiser. Sipping nothing stronger than Lucozade, the 43-year-old says, chuckling: "My father is a hard act to follow, no question. But that's it. You can't follow. You have to go your own way. I just never felt inclined to overindulge myself in anything. It's not my way."
Harris was clearly close to his father, who died three years ago, aged 72, from Hodgkin's disease; he says that organising his memorial service is the thing of which he is most proud. He recalls with awe the way his father handled the more intrusive elements of the press. "I always remember when he was being interviewed about Pirandello's Henry IV, which is about someone who invented a personality for himself. Dad said: 'Of course, I invented Richard Harris.' What he meant was that he would play up to the press whenever he needed to sell more tickets. He'd go and cause some headlines. It was great fun, but it was all a deliberate act."
Harris was always encouraged by his father to become an actor after Richard saw him perform in Entertaining Mr Sloane at Duke University, in North Carolina. "I remember him coming back stage with a big, big smile and saying: 'You've got it!'"
The son would be the first to admit, however, that it has not always been easy following in the footsteps of such a fêted father. "One of the problems I had starting off is that I went up for auditions with directors whom dad had recently fired. During Henry IV, he got through three or four directors. I remember walking into an audition with one of these men and he said: 'Are you...? Oh my God, you are!' After the audition, I never heard a word from him. So when you ask if it helped having a famous father..."
Despite such setbacks, Harris has built an impressive career in independent films such asI Shot Andy Warhol, Sylvia andThe Other Boleyn Girl. He concedes that his choice of art-house pictures has not always given him the highest profile. "A big fat hit now and again would be good. But I've done a lot of indie films because it's the sort of material I'm interested in."
Harris, it seems, is not about to sell his soul to Hollywood. "The sorts of parts, even if you're playing the main guy, in one of those stonking blockbusters are really tedious. They're very, very simple cardboard characters who mostly just have to glower, smoulder and say witty lines quietly. They're not human beings at all; they just don't resemble anybody."
And with that, Jared Harris takes one last, defiant swig of Lucozade.
'To the Ends of the Earth' starts at 9pm on Wednesday on BBC2Reuse content