"Straight off the plane," he tells me, spreading his considerable bulk across a settee at the Dorchester, "and I wasn't even allowed to sleep. I had to rush over to Hamleys. I've got a 20-month-old son who at this very moment will be at home in New Zealand watching Toy Story. So I had to find a Buzz Lightyear for him. Do you have any idea how impossible that is?"
His travails sprang to mind as he was in the middle of telling me how much Toy Story excited him - and how the opportunity to work extensively with computer-generated effects (not to mention a Hollywood budget) was one of the reasons why he leapt at the chance to make The Frighteners, despite the fact that he and his wife, Fran Walsh, had originally written it for Robert Zemeckis, the director of Forrest Gump and the Back to the Future trilogy. Zemeckis had been impressed by the vitality and imagination of Jackson's early, low-budget gore-fests, and agreed instead to act as executive producer, using his considerable clout to help steer The Frighteners through Hollywood's shark-infested waters. The standard stories of studio interference are conspicuous by their absence; true to his word, Zemeckis got the film made exactly as it was written.
You may not appreciate quite what a feat that must have been until you see the picture. It's a twisted ghost story with Michael J Fox as a con man living with a trio of ghosts who aid his scams by haunting local residences, only for him to turn up and perform dubious and very costly exorcisms. Out of this initially comic scenario comes something altogether more chilling: local people are being picked off one by one, and this series of bizarre deaths begins to look like the work of an aggrieved spirit from the other side. The film starts out making you chuckle, then has you feeling a touch uneasy, before finally pinning you to your seat with fear. It is not - repeat, not - the Ghostbusters clone suggested by advance publicity. Jackson believes that this may be one of the reasons for its poor performance at the US box-office.
"The easiest way to promote a film to the public is to make them think it's a bit like something they've seen before," he explains. "The trouble with The Frighteners is that even if you said it was Casper meets Natural Born Killers meets The Silence of the Lambs, you're no closer to knowing what to expect. And it was promoted, quite wrongly, as a horror-comedy.
"When it starts to get tense and scary, that confused a lot of people. Of course, the fact that it didn't go down as well as we hoped may have something to do with Universal bringing its release date forward from Hallowe'en to the summer, so that we were competing with Independence Day and Twister. Oh, and the first day of the Olympic Games. You could say that the odds were stacked against us. It's doing very well outside the States, though - the film has a dark, satirical tone that is much better suited to European sensibilities."
Just as Heavenly Creatures, the true story of two schoolgirls whose obsessive friendship drives them to kill, was the last thing any fan of Jackson's early work might have expected him to make, so The Frighteners marks yet another move that will confound anyone who thinks they've got the director figured out.
"I'm at a point in my life now where each time I make a film I'm trying to set myself new challenges," he says firmly. "My first three films were all different from each other, but I felt very strongly after Braindead that I was getting into a rut. I'd created something that people kept expecting me to do, again and again. When I made Heavenly Creatures, it wasn't that I had lost interest in horror - I've always had a great love and affection for the genre. I could easily have gone on and had a nice comfortable niche as the New Zealand splatter director, but I wanted a challenge because that's the thing in life that ultimately provides the most satisfaction and sense of accomplishment."
Don't you despair of the current frail state of the horror film?
"Oh, I don't think we need to worry about it. Historically, horror movies operate in cycles of 10 or 15 years. The last really important wave was in the late-Seventies and early-Eighties, films like Dawn of the Dead and Re-Animator and The Evil Dead. There were things there that you just couldn't believe you were seeing, things that went further than anything in your imagination. Those guys created the splatter film, and when I made Braindead, that was my way of showing what a fan I was.
"Horror's a great genre if you're a film-maker without much money and you want to make a big impact. What's happened over the last few years is that the young directors doing their first films have veered much more toward social realism. Ten years ago, they would all have been making horror films, with their buddies doing the special effects. Now it's more fashionable to do slice-of-life movies. My favourite quote of all is from Hitchcock: 'Other people's films are slices of life. Mine are slices of cake.' That's the way I feel, really."
Jackson's biggest challenge is yet to come. Universal was sufficiently impressed with The Frighteners to sign him up to direct a new remake of King Kong. He and Walsh have finished the script, and you can see by the way his face lights up when he talks that he can't wait to sink his teeth into it. But there's one question that should greet any remake. Why?
"There is a logical reason," he shrugs, "which is sad but true. There's a whole generation of young people who would never bother to look at the original version. If it's made in 1933, in black and white, with scratchy sound and jerky stop-motion animation, then they're not even going to watch a minute of it. That makes me really sad.
"The challenge for me, of course, is that I'm in a no-win situation. I'm remaking a classic that everyone - perhaps rightly - will say should be left alone. People came to Heavenly Creatures without preconceptions, but that won't be the case with King Kong. There's no critic in the world who's going to open their review of it with 'This far surpasses the 1933 version...' Even in my wildest dreams, I know this isn't going to happen."
He laughs like a madman, or a genius.
"I'm set up to lose!"
'The Frighteners' opens tomorrow