It's difficult now, given the city's reputation for liberalism and excess to imagine Amsterdam in the years following the second world war. It was a dull, staid place where, as Albert Camus wrote in the Fall, published in 1955, "for centuries, pipe smokers have been watching the same rain falling on the same canal".

Yet within a decade it had become the heart of the youth revolution and had begun to nurture revolutionary ideas. Among them was Ajax, a football team that if not the greatest there has ever been, was almost certainly the most influential. Speak to Arsène Wenger or Arrigo Sacchi, Marcelo Bielsa or Pep Guardiola, and all, to an extent, have drawn their philosophies from the team created by Rinus Michels.

As David Winner demonstrates in Brilliant Orange, Dutch football in the time Camus was writing of was dismal. The national side won only two of 27 internationals between June 1949 and April 1955 but the coming of professionalism in 1954 provided a stimulus. It was a culture with few preconceptions and little to lose; it was open to change. Ajax's revolution was the development of pressing – independent from and simultaneous with the same process being enacted under Viktor Maslov at Dynamo Kyiv.

It's a style of play that requires great physical preparedness – it would have been impossible in an amateur context. By the time of Michels, not only was professionalism established, but the shortages of the war years were over, nutrition was good and sports science (both legal and illicit) had advanced sufficiently that players could keep running for 90 minutes.

The seeds of Ajax's development had been sown by Jack Reynolds, who had played for Grimsby, Sheffield Wednesday and Watford before moving to Switzerland in 1912. He had three stints as coach of Ajax, the last of them immediately after the war, which he spent interned in a camp at Tost, where PG Wodehouse was also detained. Reynolds believed in attacking, passing football and ensured all levels of the club played in the same style. One of his pupils was Michels.

It was only in 1959 with the appointment of Vic Buckingham, schooled in the best passing traditions by Peter McWilliam at Tottenham, that the seeds began to sprout. Six years later, he was succeeded by Michels, who led Ajax to the title in his first season. That this might have more than local significance was demonstrated the following season as they thrashed Liverpool 5-1 in the European Cup.

Still the style was developing. Michels had changed the shape to 4-2-4 and encouraged a passing, possession-based game, but there was no sense of systematised pressing at that stage. There was, though, a radicalism in the air. Amsterdam in the 1960s was, as the British anarchist Charles Radcliffe put it, "the capital of the youth rebellion". Provos, dressed all in white, staged anti-consumerist demonstrations and art became increasingly avant garde.

The key moment came in 1966 with the wedding of Princess Beatrix to Claus von Amsberg, a German aristocrat who had served in the Wehrmacht. Police set about protestors demonstrating against their marriage with batons, prompting such revulsion that tolerance became official policy. Within a couple of years Dam Square had become a camp for foreign hippies and the Amsterdam police had a reputation as the most easy-going in Europe. It is no coincidence that it was at the Amsterdam Hilton in 1969 that John Lennon and Yoko Ono celebrated their marriage with a week-long bed-in.

Perhaps there were no direct links between the Provos and Ajax but the football of Ajax developed in an age when questioning the orthodoxy was the norm; everything could be challenged. Johan Cruyff became an icon of the burgeoning Dutch youth movement of the time. In 1997, in a piece in Hard Gras magazine marking Cruyff's 50th birthday, the journalist Hubert Smeets wrote that: "Cruyff was the first player who understood that he was an artist, and the first who was able and willing to collectivise the art of sports". In a piece in issue three of the Blizzard, Simon Kuper and David Winner argue that Ajax played the same role in the Netherlands as the Beatles played in England. "The Dutch," Smeets went on, "are at their best when they can combine the system with individual creativity. Johan Cruyff is the main representative of that. He made this country after the war. I think he was the only one who understood the sixties."

That notion of individuality within a system was characteristic of the Netherlands at the time. Indeed, the prefix "totaal", first attached to football after the performances of the national team at the 1974 World Cup, was used across a range of disciplines to express that relationship between individual and system. The architectural theorist JB Bakema, who wrote for the influential Forum magazine, spoke of Total Urbanisation, Total Environment and Total Energy. "To understand things," he said in a lecture given in 1974, "you have to understand the relationship between things … Once the highest image of interrelationship in society was indicated by the word God; and man was allowed to use earth and universal space under condition that he should care for what he used. But we have to actualise this kind of care and respect since man came by his awareness nearer the phenomenon of interrelationship called the relation of atoms. Man became aware of his being part of a total energy system."

After beating Liverpool in 1966-67, Ajax lost to Dukla Prague in the quarter-final, something that prompted Michels to reshape his defence, bringing in the tough Serbian sweeper Velibor Vasovic from Partizan. Ajax won the league four times between 1966 and 1970, and also lost in the final of the European Cup to Milan in 1969. It was that achievement that captured the imagination of the Dutch public, with over 40,000 travelling to Paris to watch a play-off against Benfica after Ajax had overcome a 3-1 deficit from the home leg to draw 4-4 on aggregate in the quarter-final. "I played the last man in defence, the libero," said Vasovic. "Michels made this plan to play very offensive football. We discussed it. I was the architect, together with Michels, of the aggressive way of defending."

The pressing aspect stemmed largely from Johan Neeskens's aggression. He was usually deputed to pick up the opposing playmaker and the coach Bobby Haarms described him as being "like a kamikaze pilot" as he pursued him, often deep into opposition territory. At first other Ajax players hung back, but by the early 1970s they had become used to following him. That meant they were playing a very high defensive line, squeezing the space in which the opposition had to play. That was risky, but Vasovic was adept at stepping out to catch opposing forwards offside.

Vasovic was a rarity. Most of the side had grown up together through the academy and so became capable of what Buckingham called "habit football", instinctively knowing where their team-mates would be. The intermovement of Ajax was to a large extent organic. "When I saw [Wim] Suurbier going forward, I knew I had to go back," Sjaak Swart said. 'I didn't have to be told. And after two years everybody knew what to do."

That is not, though, to downplay the role of Michels, who oversaw and encouraged the intermovement, particularly as teams began to play with massed defences against Ajax.

"I tried to find guidelines that meant we could surprise a little those walls," he said. "I had to let midfield players and defensive players participate in the building up and in the attacking. It's easy to say, but it's a long way to go because the most difficult thing is not to teach a full-back to participate in attacking – because he likes that – but to find somebody else who is covering up. In the end, when you see they have the mobility, the positional game of such a team makes everyone think: 'I can participate too. It's very easy'. And then you have reached the top, the paramount of the development."

Shifting from 4-2-4 to 4-3-3 made that switching of positions rather easier to structure, because it tended to happen either down one flank or down the middle. So Suurbier, Arie Haan and Swart interchanged on the right; Vasovic (or later Horst Blankenburg or Barry Hulshoff), Neeskens and Cruyff down the middle; and Ruud Krol, Gerrie Mühren and Piet Keizer on the left. "People couldn't see that sometimes we just did things automatically," said Hulshoff. "It comes from playing a long time together. Football is best when it's instinctive. This way of playing, we grew into it. Total Football means that a player in attack can play in defence – only that he can do this, that is all. You make space, you come into space. And if the ball doesn't come, you leave this space and another player will come into it."

The tangible evidence that Ajax had reached the "paramount of development" came in 1971 as they beat Panathinaikos in the European Cup final, following up the success of Feyenoord a year before to mark the Netherlands as the new centre of European football. Michels left for Barcelona after that, and Ajax turned to the avuncular Romanian Stefan Kovacs. He relaxed the reins, and it was under him that Ajax probably played their best football, attacking with greater freedom than Michels had ever allowed them. "Kovacs was a good coach," Mühren said, "but he was too nice. Michels was more professional. He was very strict, with everyone on the same level. In the first year with Kovacs we played even better because we were good players who had been given freedom. But after that the discipline went and it was all over. We didn't have the same spirit. We could have been champions of Europe forever if we'd stayed together."

Certainly it was in 1971-72 that Ajax were at their most fluent, as Kovacs replaced Vasovic with Blankenburg and encouraged him, Suurbier and Krol to advance, safe in the knowledge that Neeskens, Haan and Mühren could drop in to cover. Vasovic himself always insisted Kovacs's impact was minimal. "Those who say Total Football started with Kovacs are wrong," he said shortly before his death in 2002. "Kovacs had nothing to do with it. He simply took over a very good team, the champions of Europe, and let them continue the way they had already been playing."

Such were the doubts about Kovacs that only a player revolt saved him from the sack in April 1972, shortly after a goalless draw at Benfica had confirmed their progress to a second successive European Cup final. At the time, Ajax were five points clear in the league, had just hammered Feyenoord 5-1 in Rotterdam and had reached the Dutch Cup final. "The results show that Kovacs was not wrong," Cruyff said. "Our team was ready to take part in making decisions." They went on to beat Internazionale 2-0 in the final. "Ajax proved that creative attack is the real lifeblood of the game," the report in the Times read the following morning, "that blanket defence can be outwitted and outmanoeuvred, and by doing so they made the outlines of the night a little sharper and the shadows a little brighter."

The following year, by winning the European Cup again, Ajax became the first side since Real Madrid to complete a hat-trick of titles. Appropriately, having hammered Bayern Munich 4-0 in the first leg of the quarter-final, it was Real Madrid whom Ajax beat in the semi. The aggregate score of 3-1 barely did justice to their superiority, and the tie is better remembered for Mühren's keepie-ups in the second leg at the Bernabéu, a moment of arrogance and joie de vivre that encapsulated the ethos of Kovacs's Ajax.

"I knew I was going to give the ball to Krol, but I needed some time until he reached me," Mühren recalled. "So I juggled until he arrived. You can't plan to do something like that. You don't think about that. You just do it. It was the moment when Ajax and Real Madrid changed positions. Before then it was always the big Real Madrid and the little Ajax. When they saw me doing that, the balance changed. The Real Madrid players were looking. They nearly applauded. The stadium was standing up. It was the moment Ajax took over."

In Belgrade in the final, they beat Juventus 1-0, but it was as emphatic as a one-goal victory can be as, having taken a fourth-minute lead, Ajax taunted the Italians with long strings of passes – what we might today think of as sterile domination but at the time seemed a thrilling daring way of humiliating beaten opponents.

But that was the end. Freedom became decadence and at the end of the season, in circumstances that have never been fully explained, Cruyff lost the vote to be captain. He went to join Michels at Barcelona, and it wouldn't be until he returned as coach over a decade later than Ajax again won a European trophy.