That was then... Now, Jackson is a Hollywood big shot, the sort of actor whose very name attached to a project is enough to have execs flashing green lights at it. A US entertainment magazine recently voted him joint top movie star (with Kevin Spacey). Add five noughts to the wages he got off, off, Off Broadway, double that figure, and you are getting close to the fee he commands for a film these days.
After years of struggling - as recently as the early 1980s, Jackson had the none-too-glorious role of being Bill Cosby's stand-in for the set-up shots on The Cosby Show - he has needed persuading that he has now reached the major league. Only last year, when he had the triple whammy of working on Sphere, Jackie Brown and George Lucas' prequel to Star Wars, did he allow himself the luxury of a pat on the back. "I'd worked with Dustin Hoffman and Robert De Niro, and all of a sudden, I'm standing on a set doing scenes with Yoda. I said to myself, `I've arrived'."
Putting his feet up on the windowsill in one of London's more upscale hotels - the sort of place where Hollywood stars book not just suites but apartments - the 49-year-old certainly has the easy air of someone who has made it. He is wearing a reversed black Kangol cap and smoking contentedly. Peering at me over trendy half-moon specs, or distractedly scratching his greying goatee, he has the relaxed demeanour and rich, unforced laugh of someone at the top of his game.
His success has been helped no end by the fact that he has - in the dreadful Hollywood parlance - "crossover appeal". He has attained such a status that he can now bypass the outmoded stereotypes of pimps and pushers to be cast in "colour-blind" roles. Indeed, the part he played in the actioner, The Long Kiss Goodbye, was originally written for a white actor.
Junior Simpson, a young, black British performer, for one, admires what Jackson has achieved. "I look at Samuel L Jackson and see someone who has made the transition from being a black actor to an actor who just happens to be black. Look at him in Sphere or Patriot Games - those parts could have been played by white actors, and, 10 years ago, they would have been. Steps are being made forward thanks to people like Jackson."
The man himself confirms that "I read a lot of roles that aren't race- specific. My agent sends me a lot of scripts that are just guys, not specifically African-American or West Indian. The fact that I've already done a diverse number of roles makes me more palatable".
Even now, however, Jackson is not immune to old-school Tinseltown prejudice. "Sometimes, when executives read a script and it doesn't say `African- American', they take some convincing that I'm the guy who can do that. When my name comes up, it's `oh, my God, I hadn't thought of him'. But the world does have people like us in it. We do do almost every job that's out there. Sometimes, you look at a movie and say, `where are we?' How can you shoot, say, a Woody Allen movie in a city as large as New York and still say, `where are the ethnic people?' It's strange.
"Prejudice is part and parcel of the job. Other actors go through the same thing, whether it's because they're young or blond. A lot of the people in suits who make these decisions are very narrow-minded. They're business rather than creative people. They're part of show business - with the emphasis on business. Some people perceive it as a slight, but understanding who these people are prevents me from being frustrated by it."
After years of well-regarded, but lower-profile supporting parts in such films as Ragtime, Jungle Fever, Sea of Love, Coming to America, Do the Right Thing and GoodFellas, Jackson was thrust centre-stage by his role as the Scripture-quoting black-clad assassin, Jules, in Quentin Tarantino's wildly culty Pulp Fiction. The jury at Cannes liked Jackson's performance so much they created the new award category of Best Supporting Actor especially for him.
Jackson reckons the film struck such a chord because "Quentin gave people something new and unique, so they felt refreshed by it. We're fed the same thing so much by the Hollywood machine that when something like this comes along, it's engaging. Plus, Quentin is a consummate thief. He has watched so many films, and has this amazing facility for remembering specific scenes. He can mix'n'match from them so you think you're watching them for the first time".
He went on to star as an equally unsavoury character - this time, an arms dealer - in Tarantino's next opus, Jackie Brown. "My characters in his films are very verbal and theatrical. You know how they feel, and they're very personable people. No matter that they have antisocial jobs, they're acceptable as people who might live next door to you. I don't believe assassins sit at home sharpening their knives and polishing their bullets. They go to the store and drive their kids to school. They're normal people who just happen to have interesting jobs."
The only downside to his work with Tarantino was that Jackson was offered a string of Jules-alike parts. "I could've been a gun-toting, Bible-spouting fool for the rest of my career, but luckily I was able to make some other choices."
For all his hits - more recent ones have included Die Hard with a Vengeance and A Time to Kill - Jackson tries to avoid the star schtick. "I consider myself an actor rather than a movie star. As soon as you start buying into that other thing, expectations become greater. I don't want people to view me as Samuel Jackson in every role. I want them to see the character. I'd find it hard to be Bruce Willis. I service the story as opposed to being its main focus and saying `look at me, here I am'. I am not John Wayne.
"Hollywood has a tendency to repeat itself. I read a lot of scripts that are similar - you read page five and immediately know what's going to happen on page 75. The challenge is to find things that allow you to grow as an actor. It's hard to go to a Stallone film and worry whether he's going to live or die - you know he's going to live. There's never any jeopardy. I prefer jeopardy."
Which is just one reason why he chose to star in - and, for the first time, produce - Eve's Bayou, an affecting low-budget debut from Kasi Lemmons. Set in the Louisiana of the early 1960s, it is a child's view of the effect of her ostensibly respectable father's (Jackson) philandering on the rest of her family. "People like stories about people. They look at their problems and wonder how they'd react to them and relate to them. There's not a lot of nonsense in this film. There are no dinosaurs or car chases."
Jackson sets a ferocious pace, averaging five movies a year. Soon, we will see him in The Negotiator, in which he and Spacey play police negotiators, The Red Violin, which tracks a violin's history from the 16th century to the present day, and Deep Blue Sea, the new action-adventure from Renny Harlin.
He also has his eye on a script about an American who brings a designer drug into Liverpool. He was intrigued by the fact that the character wears a kilt, though worried about having to be authentic in one. "I know people don't wear anything under their kilts. It's pretty cold in Scotland, so I guess they don't have to worry about their dangly bits... "
But perhaps Jackson's most eagerly awaited role is in the Star Wars follow-up, in which he gets to say the immortal line, "may the Force be with you". So, what part is he taking in this top-secret saga?
"I could tell you," he chuckles, "but then I'd have to kill you."
"Eve's Bayou" is released on Friday