In the olden days, press releases landed at The Independent travel desk with a thump. By the sackload. The analogue predecessor of repeatedly hitting the delete key involved painstakingly opening each envelope, skimming the first couple of lines of the announcement and then binning it.

In October 1995, though, one press release caught my eye. “EasyJet £29 airfare makes flying as affordable as a pair of jeans” read the headline. The fact that the message was printed on bright orange paper helped it stand out, too.

Reading on, it seemed that The EasyJet Airline Company planned to revolutionise aviation in the UK.

“The airline is starting three daily services (two daily at the weekend), with Boeing 737s, between London Luton and Glasgow International Airport on 10 November 1995, and three daily services (two daily at the weekend) to Edinburgh will commence two weeks later on 24 November 1995.”

It seemed sadly obvious to me that, as with so many airline start-ups before and since, the venture was doomed to failure. A one-way fare of £29 from London to either of the two biggest Scottish cities was preposterously low. The prevailing lowest return fare from Heathrow, on both British Airways and its rival British Midland, was over £100. And those incumbents made a fortune by charging hundreds of pounds return for business travellers who were not staying in Scotland over a Saturday night.

“We have spent a lot of time researching how to make our fares affordable to everyone while making air travel convenient and fun,” said the chairman and chief executive, Stelios Haji-loannou.

EasyJet made clear that £29 was the lead-in price, and that fares could rise as high as £59. Yet this was a fraction of the sums commanded by its established competitors. What’s more, the airline didn’t seek to segment the market by insisting on that despised “Saturday night stay” rule for cheap tickets. Whether you chose to visit London from Edinburgh for a day, or fly one way and take the train the other, the fare stayed the same.

There’s undercutting, and there’s commercial suicide, I concluded. The only question was how long easyJet could survive before the cash ran out. Initially, it had to borrow planes. The Boeing 737s were chartered in from another airline, GB Airways. At the controls of the first flight: Captain Fred Rivett, who happened to be on secondment from British Airways.

As BA will have noticed, easyJet is very much still in business. It has more than 350 Airbus A320 jets, 1,207 routes linking 164 airports in 38 countries and a market capitalisation of £3.58bn.

So where did it all go right?

The first few months, rocky for any airline, were helped by Stelios having deep pockets; his father, a Greek shipping billionaire, helped out with a £5m loan. Helpfully, the entrepreneur was also a super-smart visionary.

In the mid-1990s, the UK and the rest of Europe were deregulating aviation, adopting the then novel concept of allowing airlines to fly where they chose and charge whatever fares they wished. Stelios saw an opportunity to democratise flying, and seized it.

With no airline background to burden him with convention, he could cheerfully decide to cut out the middleman: travel agents who, at the time, took a healthy cut of the price of a ticket. Catering ceased to be a cost and instead became a revenue stream: cup of tea, 50p. He recruited formidably good people, a tradition that continues today. And he cut a deal with Luton airport that rewarded growth with low airport charges.

In the early days, some travellers were nervous about flying with a budget airline: surely the carrier must be cutting corners? Fortunately, easyJet has demonstrated it is so risk-averse that it is now the second-safest airline in the world in terms of the number of passengers flown without a fatal accident.

Only Ryanair has done better. The Irish carrier now flies around twice as many passengers as easyJet, and is seven times more valuable, according to the markets.

Yet easyJet has worked wonders for British travellers by spurring ferocious competition that is still delivering rewards. The lowest easyJet Luton-Glasgow fare in 1995 was £29 – equivalent to £71 today. Yet anyone who wants to fly the route this month can easily find a fare of £27.

EasyJet has created vast social and economic benefits; the environmental cost of flying without frontiers is another matter. But today’s aircraft are far quieter and more efficient than the Boeing 737 in which Captain Rivett, Stelios, passengers and crew roared down the runway on 10 November 1995.

To my considerable regret, I was not on board. But I have made up for it since, enjoying endless “convenient and fun” air travel at fares that, 30 years ago, were beyond the traveller’s wildest dreams.

Thanks for the memories you have helped to create, easyJet. Many happy returns.

Simon Calder, also known as The Man Who Pays His Way, has been writing about travel for The Independent since 1994. In his weekly opinion column, he explores a key travel issue – and what it means for you.