The stocky, cheerful Haji-Ioannou is the latest in a long line of entrepreneurs who have decided to shake up air travel. He started his own airline, easyJet, last November and is busy raising its profile in the most aggressive way he can. His headquarters at Luton are painted orange; so are his aircraft, the only ones in the world with huge telephone numbers on their fuselages. His (orange) advertising is less than subtle, too: it is designed to irritate travel agents - whom he does not use - and to tell you loudly that easyJet will sell you a flight ticket for just pounds 29.
But Haji-Ioannou is unusual in other ways. He is probably the only airline proprietor who also owns a shipping line. He is probably the only airline proprietor who has yet to reach his fourth decade - he is 29. And he is certainly the only airline proprietor who has a possible 12-year sentence for manslaughter hanging over him.
Which leads us back to that yacht. EasyJet has so far spent pounds 25m, all of which has come from Haji-Ioannou's family. His father, Loucas, came from a poor family in the Troodos mountains of Cyprus. He bought his first ship in 1959 and, with a stroke of bold counter-cyclical buying in the 1980s, built up the biggest tanker fleet in the world.
As a result Stelios, his brother Polys and his sister Clelia were born with solid platinum spoons in their mouths. This explains the yacht, but does not explain why he works 16 hours a day rather than wallowing full time in the good life. "I've always been conscientious and hardworking," he says. "I've never wasted time." There is also, he says, an element of proving himself to dad.
The next question is: why has he moved into airlines, an industry that has destroyed more bold ambitions than any other?
Why, in particular, has he decided to "do a Laker" - a doom-laden expression if there ever was one - by competing entirely on price?
To answer that, we need to look at Haji-Ioannou's career so far. He was brought up in Athens and, when he was a teenager, decided he wanted to set off on a well-trodden path for wealthy Greeks - to London, and specifically to the London School of Economics. After getting an economics degree, he took a masters in shipping, trade and finance at City University Business School. In the process he was so indoctrinated in business school practices that he grew impatient with the Greek way. "I like organised things," he says. "I don't like the corruption and slowness of Greece."
Leaving London in 1988, he joined his father's business. "I imagined I would spend all my life in shipping," he says. But he had been seriously infected with business-schoolitis and soon found himself drawing up a plan for his own company. It would be for up-market tankers, which would carry more valuable products and thus charge higher rates. Where most business school graduates would leave their model on the computer, he was in a position to translate it into solid steel. Dad came up with $50m and, in 1992, Haji-Ioannou set up Stelmar. The year before this, however, disaster struck. A giant Troodos Maritime tanker, the Haven, blew up in Genoa harbour killing five crewmen and creating one of the Mediterranean's biggest environmental disasters. Stelios, still only 23, found himself accused with his father and another executive of manslaughter.
The Italian legal process is still grinding through. "Early on, it was like a sword of Damocles," he says. Now he is more relaxed; he expects the civil action to be settled in about six months and the criminal case to be dropped at the same time.
Haji-Ioannou claims the accident has made him obsessive about safety. "It taught me that you should always prepare for the worst."
He spent a couple of years building up Stelmar before the market flattened and then decided it was time to do something a little more exciting. Friends in Athens who ran a Virgin franchise asked him to invest in their operation. He was unimpressed but sufficiently intrigued to start producing business models for a possible new airline.
He travelled to the United States where he was particularly taken by the relentlessly profitable South West Airlines in Dallas. It used a combination of rock-bottom costs and rock-bottom fares to attract people who otherwise would not be able to fly. Haji-Ioannou reckoned the same approach could work in Europe because, as he explains in business-speak, "the elasticity of demand for air travel is greater than one". In other words, cut the price and extra passengers will more than make up the revenue.
He returned to his spreadsheet and developed the business concept that became easyJet. Once again his father agreed to help him, with pounds 8m to capitalise the company. EasyJet started flying between Luton and Scotland last November and has already sold 250,000 seats. It is now expanding its routes - to Amsterdam, Nice and Barcelona. "My father doesn't know about airlines but he's proud of me," Haji-Ioannou says.
The phone number on the fuselage is a clue to his central tenet: cut out the travel agent. "The traditional ticketing system is great if you need flexibility but it adds a layer of cost," he says. Unless you intend to change planes, you do not need the flexibility a traditional IATA ticket brings. Get rid of the ticket and you have escaped the airline reservation systems and, with them, the travel agents plugged into them. "The whole concept of the travel agent is absurd," he says. "They appear to be agents of the traveller but are actually agents of the airlines." EasyJet, he says, is the only airline that has never paid a penny to travel agents.
Without agents, he has to rely on direct sales - which explains the phone numbers and the pounds 2m he has spent on advertising. Passengers ring up, pay by credit card, and are sent a receipt with a confirmation number. When they turn up at the airport they give the number, show identification, and off they go.
His obsession with abolishing paper goes beyond tickets. Every document that comes into his headquarters is scanned into the computer system, then binned. His entire administrative staff of 12 people fits in one room - he in one corner, his finance department of two in another.
The other big cost saving is to use Luton, which has been losing scheduled airlines and is offering rock-bottom landing fees. "The differential with Heathrow is pounds 10 per passenger," Haji-Ioannou says.
The pricing system is real business school stuff. If you book early for a Scottish flight, you pay pounds 29 one way. The later you book, the more you pay - up to pounds 59. EasyJet ratchets up the more popular flights fast, so to get a pounds 29 ticket on a busy Friday flight, you would have to book weeks ahead. On a mid-week flight, you might still get it the day before. Haji-Ioannou says that half the tickets sold so far have gone for pounds 29 - though passengers might be upset to find that there is also a pounds 5 airport tax.
The choice of routes is important. "We aim for those with high prices, reasonable volume and little competition," he says. UK domestic routes fit the bill but why the highly competitive London-Amsterdam? "It's the biggest route from London after Paris," he says. "And our price - pounds 35 - is particularly cheap for people flying from Holland." Nevertheless, some travel industry experts are worried that easyJet may be expanding too fast into routes in which it does not have a sufficiently clear price advantage.
Haji-Ioannou has just paid pounds 17m for a relatively youthful Boeing 737, and is keen to emphasise the safety of his three-strong fleet. "If you think safety is expensive, try an accident," he says with some feeling.
He is not, he says, concerned that he will crash land as did Freddie Laker ("a bit of a legend for me"). His computer tells him his model works better on short-haul than long-haul flights, and he does not believe he will be troubled by dirty tricks from other airlines. "BA has learned its lesson," he says.
When easyJet is established, history suggests he will look for something else to do. "When we get to eight or 10 aircraft, it could be the right time to float," he says. Judging from his other interest, it seems likely he will head off computerwards.
This weekend he is flying to Athens and hopes to spend time on his yacht. He will travel with British Airways. Would it not be convenient if easyJet flew to Athens? "It doesn't fit into our model," he says. Business school 1; Greece 0.