Two men sit shoulder-to-shoulder against a bright white wall. They are young and cheerful, at ease in each other's company. They clown around, try a hat on for size and direct dopey grins at the camera. The prevailing mood is one of jollity, and yet what we are witnessing are the rushes from a martyrdom video, shot at Osama bin Laden's farmhouse in January 2000. The man on the right is Mohamed Atta, ringleader of the 11 September hijackers. His buddy on the left is Ziad Jarrah, who piloted the United 93 flight that came down in a Pennsylvania cornfield, killing everyone on board.

Fast-forward a decade. Chris Morris and I are sitting shoulder-to-shoulder in a London production office, staring at the screen of a scuffed white laptop. "It doesn't conform to type, does it?" Morris says. "These aren't cold, reptilian killers. They're dicking about with a hat; they're pissing themselves laughing. What's interesting is to look at this footage and think, 'But they still did it.' They acted like this, and then they still went and did it. And if you keep going with that line of thought, you might get somewhere and come out the other side." He shrugs. "Or maybe you just get lost and go completely mad."

Morris has spent the past five years researching, scripting, shooting and editing a comedy about suicide bombers. He has gone with it, got through it and come out the other side, and if he's gone mad in the process, it is sometimes hard to tell. In the course of a chaotic three-day spell, I run into the director on several occasions and he's different every time; by turns bouncy and ebullient, caustic and contemptuous, professional and forthright. At each turn in the conversation, I think I catch glimmers of the myriad media ghouls he once channelled on the likes of Brass Eye and The Day Today. Then again, maybe not. Morris suggests that his days of deconstructing the antics of the fourth estate are now behind him. He has grown up, moved on. Right now, he has other fish to fry.

Four Lions is a bumbling picaresque about a quartet of would-be jihadis who hatch a plot to bomb the London Marathon. It introduces us to jittery Omar (played by Riz Ahmed), dozy Faisal (Adeel Akhtar), foursquare Waj (Kayvan Novak) and belligerent Barry (Nigel Lindsay), while an inept rapper named Hassan (Arsher Ali) jogs on the sidelines, awaiting his big chance. The film's early scenes set up the jihadis as a bunch of Dad's Army-style buffoons – hapless, misguided, even faintly lovable. Then, about midway through, one of them runs through a field, stumbles over a wall and blows himself up (Asian Man's Head Falls Out Of Tree, proclaims the headline in the next day's paper). After that, we twig that this gentle, domestic excursion is actually tilting towards oblivion. And this, surely, is the point of Four Lions. It is a film on a knife edge, one that pits the inherent humour of its situation against the inherent horror of its subject matter.

"Big thinking in small places," agrees its director. "It's a fairly standard comic position." In person, Morris is lithe and limber, with a corkscrew bouffant and a birthmark on his cheek that the tabloids have chosen to read as the mark of Cain, physical proof of an evil nature. If so, it seems to agree with him. Morris is now in his late 40s, though he seems preternaturally boyish – more youthful, somehow, than the Paxman-esque news anchor he first road-tested on the BBC back in 1994.

He explains that he was first drawn to the idea of suicide bombers after completing work on his infamous Brass Eye paedophile special from 2001. The research, he says, predated the London bombings of 7 July 2005. "It was an attempt to figure it out, to ask, 'What's going on with this?' This [the "War on Terror"] is something that's commanding so much of our lives, shaping so much of our culture, turning this massive political wheel. I was wondering what this new game was all about. But then 7/7 hit that with a fairly large impact, in that we were suddenly seeing all these guys with a Hovis accent. Suddenly you're not dealing with an amorphous Arab world so much as with British people who have been here quite a long time and who make curry and are a part of the landscape. So you've got a double excavation going on."

And what conclusions did he draw? It strikes me that modern jihad (or at least the version that we see in Four Lions) says as much about the west as it does about the east. It's an unholy hybrid, isn't it? Fundamentalist zeal by way of Fame Academy.

"Well, it could be," Morris says, though he is not wholly convinced. "There are a lot of theories, all partly right. You could argue that this is a version of celebrity culture gone wrong. There's certainly a Live Aid element to it." He smiles. "I'm not saying that Diana was the perfect suicide bomber. But there are some parallels, I think."

I first spoke to Morris about seven years ago, when he granted a brief phone interview to promote his Bafta-winning short film My Wrongs 8245-8249 & 117. At the time, I presumptuously suggested that the ongoing War on Terror seemed tailor-made for a Brass Eye special. Except he was having none of it. There was no mileage in the idea, he sniffed. He didn't know what could be done with it.

Today, he qualifies that position. OK, he was interested, even back then. It's just that the Brass Eye approach had begun to bore him. "You can only maintain your interest if you're travelling more in ignorance than knowledge. I did formalise some ideas, but the jokes were all concerned with media coverage and perception, rather than the issue itself. And when you've already had a crack at media language, you can only do it a few times before you know how it works."

He thinks it through. "It's an age thing as well. You see young people, or kids, and they're fascinated by the way people talk. And that's great. But eventually you get to the point where you think, 'You know what? I don't care how you talk, I'm just listening to what you're saying.' "

All of which makes Brass Eye sound like an inspired piece of juvenilia. "Well, maybe," he says. "And, of course, there's a place for looking at the language. How can you wage a war on terror? How can you declare war on an abstract noun? But the danger is that then you're ignoring the most interesting thing about it. This is such a life-or-death issue that just looking at the language would be a cop-out. You want to find out what's behind the rhetoric. You need to look at the engine."

So Morris pushed his satire in a fresh direction and plunged himself into years of detailed research. He sifted through court transcripts, interviewed experts (and idiots) in the field, and came away with a stash of anecdotes that sound at least halfway as hilarious as anything that appears in the finished film. He tells me about the BNP hard man who "accidentally converted himself" after reading the Qur'an; about the fundamentalist who demanded that the world be run under a caliphate, yet freely admitted that he was unable to apply Sharia law in his own home because his wife wouldn't let him. Some of his subjects, he adds, were really rather funny. "The thing about a sense of humour is that it's not bestowed on the good. It's just randomly dished out. People say that Abu Hamza is very good at jokes. Admittedly, Bin Laden doesn't really do jokes. Maybe that's because his writers are no good, or his sense of humour is too dry for western tastes." He sighs. "Certainly he's no worse than Gordon Brown."

The homework has paid handsome dividends. Four Lions is a good film, both audacious and insightful. But it is also – and there's no easy way to gloss this – a potentially hazardous one. I ask if Morris is concerned about possible reprisals, and he umms and ahhs. Yes, he was nervous about previewing it at the Sundance film festival, and then again in Bradford, but so far the response has been positive. If anything, he is more concerned with upsetting those who were caught up in 7/7, except that he has spoken to someone who was on one of the tube trains and they claimed to be OK with the idea, "so long as it's funny". Besides, he adds, there is no way of making a film that's 100% fatwa-proof. During his early days as a radio DJ, he once bungled a request, played Tony Bennett instead of Frank Sinatra, and went on to receive lurid death threats from a listener in King's Lynn. Who can tell what people will react to?

To his detractors, Morris remains a malign and shadowy hoaxer; a hit-and-run media terrorist whose dislike of the limelight is taken as cowardice. Away from the cameras, he lives quietly with his wife, literary agent Jo Unwin, and their two young sons. He rarely attends public events and almost never gives interviews which, inevitably, only fuels the mystique. When embarking on Four Lions, he corralled the services of two co-writers, Peep Show creators Jesse Armstrong and Sam Bain. For them, part of the appeal was the chance to meet Morris in the flesh. "We wanted to check he really existed," Bain tells me. "He has this reputation as the dark lord of comedy, this godlike presence. It was a surprise to find that he's actually human."

Morris has insisted that he never deliberately courts controversy; that there's no purpose in tackling a subject if your sole aim is to shock. That said, it seems clear that his compass is naturally pointed towards the thorny and the taboo. I keep coming back to that paedophile special, in which a series of duped celebrities lined up to talk "Nonce Sense" and earnestly explain that you can tell when your child had been abused because they "smell like hammers". Of course, what Morris was lampooning was the media's collective hysteria about paedophilia, as opposed to paedophilia itself. But no matter. The show sparked a perfect storm of tabloid outrage. The Daily Mail dubbed Morris "the most loathed man on TV", while 2,000 viewers (or possibly non-viewers) rang up to lodge a complaint with Channel 4.

And what was Morris's reaction to all of this? Was there, perhaps, a part of him that relished the attention? "I didn't relish it," he says quietly. "What happened was that I'd gone on holiday. I'd gone on holiday by mistake, in relation to the transmission time. Channel 4 had bumped [Brass Eye] by three weeks because there was a girl who had gone missing on a school trip in France, so it coincided with my holiday and I flew right back into the storm." Another shrug. "It sounds dismissive, but it was actually pretty boring. It wasn't particularly novel."

It wasn't novel, being the subject of a witch-hunt? "But it wasn't a witch-hunt. It all seemed to happen in a fictional world. I mean, if I'd gone on the tube and been menaced by a lot of angry people, then it wouldn't have been boring and it wouldn't have been pleasant. But stuff that's going on in the papers when you've just done a show about stuff that's going on in the papers is just" – he grins – "stuff that's going on in the papers."

Interview over, Morris reboots his laptop, guides me past various folders ("Asian Girls Names") and shows off some exclusive Four Lions off-cuts. En route, he name-checks the films he used as touchstones. He thought of The Ladykillers, The Guns Of Navarone and a thriller by Gillo Pontecorvo called Operation Ogro, about a true-life band of Basque separatists ("Like this, but without the jokes"). Now look, here's some behind-the-scenes footage, interspersed with multiple takes of key sequences. His work is now over, but he seems loth to let it go. "Did you know that Terrence Malick is still working on The Thin Red Line? Ten years after it was released in the cinema." How typical of Morris, to set his stall beside another famous recluse, another man who prefers to toil in the shadows and let his work speak for itself.

On screen, Omar is squabbling with Barry. This, Morris explains, is an exchange that failed to make the final cut because it was seen as being too obvious, too explicit; too much thought and not enough joke. "Sometimes you got to do the wrong thing in order to do the right thing!" Omar is screaming. "Sometimes the wrong thing's more right than the right thing!"

I leave with the suspicion that I've just witnessed the moment that best sums up the comedic intent behind Four Lions. Perhaps it says something about the man who made it, too.

• Four Lions is released on Friday.