Sepp Piontek was walking through the team hotel in Querétaro when he heard some of his players confirm what his instincts told him: that they were starting to become homesick. Denmark had won the Group of Death – almost a tournament within a tournament at the 1986 World Cup − in stunning style. What more could any self-respecting Dane ask for? “I heard them say they had done very well,” says Piontek, “and if they now had problems it was not so bad and they could go home and have holidays.”

Trust is good but control is better. Piontek tried to regain control by giving a speech that was pitched somewhere between Churchill and Hollywood. For some of the players the memory is vivid. “I remember it very well because it is something you can really use as a manager,” said Michael Laudrup. “He said, ‘I know some of you are tired. You want to win tomorrow, but if you don’t, well, you are tired. Some of you are tired physically and all of you are tired mentally. I want to tell you one thing: we are Denmark, we are not West Germany, we are not Italy, we are not Brazil. For some of you, maybe for all of you, this will be the first and the last time you will ever participate in a World Cup.’

“I remember that, because the next time Denmark played a World Cup, 12 years later, there was only one player [from that team] left: me.” It stayed with Laudrup; he gave a similar speech to his own Swansea players before their Capital One Cup final victory over Bradford in 2013.

Laudrup was the centre of attention before the second-round game against Spain. He had turned 22 three days earlier. Two years before, Denmark had beaten Yugoslavia 5-0 the day after his 20th birthday. “It would be fantastic if we could do that again when we play Spain,” he said. “But the present I would really love most, of course, is the World Cup.”

His comments reflected the mood around the world, not just among the Danish squad. A banner on the streets of Querétaro needed no translation: “Dinamarca Dinamita Roja! Proxima Victima España!” They were huge favourites to beat Spain – Ladbrokes gave them odds of 4-6, Spain 7-2 – and nobody really cared that they were playing Spain rather than Morocco, which was West Germany’s reward for finishing second in the group. “After the group stage,” said Laudrup, “we thought, ‘Phwoar, we’re good, we’re good.’” Their potential quarter-final opponents, Belgium, who had beaten the USSR 4-3 in a controversial second-round thriller, were little to worry about.

During the build-up Spain’s Ramón Calderé was fined £8,000 for failing a drugs test but was not banned, with Fifa accepting his explanation that he was given medication in hospital for food poisoning. Piontek was not happy with that, or with a Fifa mix-up that meant both sides were staying in the same hotel in Querétaro. Despite an official complaint, both teams remained in the hotel; Klaus Berggreen recalls waving to the Spanish players by the pool as Denmark went off for yet another training session. Spain were pretty relaxed despite their formidable opponents. “Denmark play very well,” said Emilio Butragueño, “but they also let you play.” Some Denmark fans travelled home before the game, either because they had run out of money or because they had not expected Denmark to get through the group stage and had already made plans to do so.

There were the usual fitness problems before the game. Ole Qvist had recovered from dizziness but was only on the bench, Preben Elkjær needed extensive treatment for an injury he had sustained against West Germany, Jens Jørn Bertelsen played even though he was not 100% fit after his bad injury against Uruguay and John Sivebæk was ruled out of the game with a stomach bug. He had been fine when he went to bed the night before, a young man high on the prospect of a World Cup knockout match. Overnight his stomach was so bad that he told Piontek he was not sure he could play. Piontek left the decision up to Sivebæk. After much soul-searching, he pulled out. His place was taken by Henrik Andersen, which meant Jesper Olsen would move from the left wing to the right. He was in the side in place of the suspended Frank Arnesen, whom many, including Piontek, felt had been Denmark’s best player in the group stage.

Jesper Olsen, Andersen and the goalkeeper Lars Høgh were the only players who had not started against Spain in the Euro 84 semi-final. Spain had four survivors. “It’s incredible to be Danish in Mexico these days,” said the commentator Svend Gehrs before the game. “Everyone comes up to you and says Denmark will make the final.” Denmark were the better side in the first half without being quite at their best, due in part to the almost incessant Spanish pressing. They created chances nonetheless; Elkjær and Laudrup failed to force in Berggreen’s dangerous cross after an exhilarating surge and stepover from Morten Olsen; Elkjær’s arrowing long-range drive was fingertipped wide by Andoni Zubizarreta; and Elkjær hit a tired shot straight at Zubizarreta after a superb run and one-two with Laudrup.

Spain’s threat came largely on the counter-attack. Julio Alberto slashed a vicious cross onto the roof of the net and Míchel, twenty yards out, dragged an inviting square pass from Butragueño well wide.

Denmark took the lead in the 33rd minute. Berggreen found Elkjær, who changed direction superbly, waited for the run and then returned the ball to Berggreen on the edge of the box. As he played the ball, Elkjær was clobbered by Andoni Goikoetxea, who had already been booked. But the referee’s eyes were on the ball: Berggreen fell over a clumsy challenge from Ricardo Gallego and a penalty was given. “It was the Italian way of falling,” said Berggreen. “I am from the Italian school.”

Jesper Olsen sauntered up to the ball, waited for Zubizarreta to dive and passed it insouciantly the other way. Olsen was the best player in the first half, troubling Spain with a number of sinuous dribbles. One ended with a dangerous cross that was held by Zubizarreta, another with a sliced shot wide from fifteen yards. He had scored in three consecutive World Cup games, was on top of his game and looked set to keep his place even if Arnesen returned for the quarter-final.

Shortly after the goal he received a throw from Høgh on the right edge of the penalty area and, through typical sleight of hip, beat Julio Alberto without touching the ball. It was a deliciously arrogant piece of play. Høgh, like all Danish keepers in the 1980s, eschewed the long goal kick 95% of the time. This time, unfortunately, when Høgh prepared to take a goal kick with a couple of minutes to half-time, Olsen again came short to receive the ball. Høgh’s plan was to play a one-two, pick up the backpass – which was permitted in those days – and waste a little more time before the interval. As he rolled it out to the right of the area, Julio Salinas came to press Olsen, who swaggered past him with a stepover and began to move upfield. Høgh stayed where he was, thinking Olsen would play the ball down the wing, and all the Danish defenders started to trot upfield.

Olsen, believing Høgh had moved back to a central position, played a blind square pass across the face of the penalty area. There was a man there, but it wasn’t Høgh: it was Butragueño, who had smelt something. As Høgh ran desperately across the face of the goal, Butragueño opened up his body to slip the ball through Høgh’s legs and into the net. Svend Gehrs’s commentary captured the national mood: “Jesper, Jesper, Jesper, that one is lethal.” Busk, who had been running the other way before hearing the alarm call from his teammates, wondered, “What the hell just happened?”

“I would never have done anything else,” said Olsen. “I already knew before the ball came what I was going to do. It’s just one of those things. The manner in which it happened maybe sucked it out of the team a little bit.”

Two of the strengths of the team – short goal-kicks and players expressing themselves with the ball – had become a weakness at the most important time. Had Spain’s Tomas not drilled one of the worst crosses of the entire World Cup miles over the bar, Denmark would not have had a goal-kick. Had Arnesen not been suspended, Jesper Olsen would not have been playing. Had Sivebæk not gone down with sickness, Olsen would not have been on that side of the pitch to receive the ball from Høgh. “I take my share of the blame,” said Høgh. “Once Jesper went past Salinas I didn’t expect him to play the ball back, but I should have been more alert to the situation.”

The manner of the goal winded Denmark, yet by the end of the half-time break they were ready to go again. “At that point,” said Berggreen, “I was still 100% sure we would win the match.” Early in the second half Elkjær had two wonderful chances in the space of 45 seconds. The first might have been the defining goal of his career. He set off on a diagonal run from the halfway line in which he beat Tomas twice, first with strength and then with balance, roared past Goikoetxea, dismissed Gallego with a hand to the throat and finally, from the edge of the area, smashed a shot that got stuck between Zubizarreta’s legs.

Elkjær was still panting moments later when he ran through on goal, despite looking offside, after a fine long pass from Søren Lerby. The ball bounced like an off-break on the poor Querétaro pitch but Elkjær should probably still have scored. He sliced his shot wide of the near post from six yards.

Those chances looked even more important when Spain scored soon after. An outswinging corner from the right was flicked across goal and headed in by the unmarked Butragueño. The defending was diabolical. Laudrup mistimed his jump at the near post; then, when the ball was flicked across goal, a number of the Danish defenders started running away from goal, allowing Butragueño to move into space six yards out.

Denmark were behind in the World Cup for the first time. Piontek went to his tried-and-trusted book of substitutions, bringing on a striker, John Eriksen, for a defender, Andersen. A similar switch had worked instantly against Belgium two years earlier; it almost did again when, after a patient eleven-pass move and a blistering run from Laudrup, Eriksen hammered a 20- yard shot straight at Zubizarreta.

Another classy run from Laudrup suggested Denmark had nothing to worry about. But when they did not equalise immediately they began to panic. Bertelsen gave the ball away in a dangerous area to Butragueño; he played the ball through to the onrushing Míchel, whose shot was saved by Høgh. From that moment, Denmark lost the plot: what was ostensibly a 3-4-3 formation was more like a 3-2-5 or a 2-3-5. Spain had a series of four-on-three or three-on-two breaks, the kind that usually only occur with two minutes remaining, not twenty-five.

One such break led to a killer third goal in the 68th minute. Denmark had five men ahead of the ball when an attack broke down, and Spain sliced them open with one long pass from Míchel to Butragueño. He was up against the last man, Busk, with nobody else within 25 yards of them. As Butragueño moved away from him on the right of the box, Busk fell over and inadvertently brought Butragueño down as he fell. It was a clear penalty. Goikoetxea rammed it in. “He falls easily, which is fair enough,” said Busk. “I just shouldn’t have touched him. At 2-1 we threw Morten up ahead of the defence and I remember all of a sudden it’s bloody quick with those counters. We gambled it all going forward way too early.”

Denmark’s street footballers lacked the necessary street wisdom. In a sense it adds to the charm. “We were a little naive,” said Morten Olsen, “but that was the way we played.” Just as they might have declared at 3-1 against Uruguay, so they might have declared and saved face at 1-3 against Spain. “At 3-1 it’s over,” said Ivan Nielsen. “You know it’s over, so it doesn’t matter.”

It unravelled quickly and embarrassingly, and Denmark were spanked. Busk, Nielsen and Morten Olsen had a combined age of 98; Spain’s three attackers – the two forwards Butragueño and Eloy, and the attacking midfielder Míchel – had a combined age of 66. Those 32 years were compounded by the furious heat. Factor in weary limbs (Busk and Olsen were two of only three Danes to play every minute in the tournament) and the lack of protection, and Denmark’s defenders had no chance, especially as Spain were thoroughly ruthless. “We have to acknowledge,” said Bertelsen, “that Spain were frustratingly good at punishing us.”

There were half-chances for the substitute Jan Mølby and Elkjær, whose irritation manifested itself in a dreadful over-the-ball challenge on Goikoetxea for which he wasn’t even booked. Denmark played the last 25 minutes with the naivety of soldiers going over the top and they were punished again when Butragueño completed his hat-trick after another four-on-three break. He was probably offside; it barely mattered.

There was no question about the penalty decision for the fifth, when Butragueño Cruyff-turned Morten Olsen and was taken down. Even though it was a clear foul, the usually calm Olsen gesticulated at the referee. Denmark’s heads had gone. So had their bodies.

“The problem came once we went behind,” said Berggreen. “We were playing at midday, you couldn’t breathe and you had trained so hard. You were so tired you couldn’t feel your legs.”

Butragueño swept home the penalty to become only the sixth man to score four goals in a World Cup match. There were 31 seconds remaining. The rest was silence.

There is a British TV archive page that lists the result as “Spain 1-5 Denmark”. At the time, those who had not seen the game nodded sagely when they were told the score. Then they were told which side had actually won. It was football’s saddest, maddest thrashing. “It annoys me tremendously still today, because it’s ridiculous,” said Elkjær. “We were the better team, but we lost our heads and that’s crazy.” Yet in a sense it was also in the spirit of Danish Dynamite. This was a team who could win 6-1 one week and lose 5-1 the next – and at Mexico 86 they became the only team since the 1950s to score and concede at least five at the same World Cup.

Spain, not for the first time, were kryptonite to Danish Dynamite. Opta stats show that Denmark had more shots and much more of the ball. Spain had 43% of the possession and scored five goals. This truly was a different era of Spanish football.

The Danish dressing-room was a combination of shock and trauma. Some players focused on a spot a thousand yards in the distance; others wept. “There was a really sad atmosphere,” said Bertelsen. “All the good football, all the goodwill and all that euphoria there was around us, all of a sudden we had to live without that. It died.” It was not just the Mexico adventure that was gone. Nobody knew it at the time, but something died in the team that day.

Elkjær tried to console Busk by telling him that he and the team had played well; that some things weren’t meant to be. Busk’s response was as heartfelt as it was concise. “My man scored four goals.” 30 years on, Busk can see the funny side. “We were faced with these quick strikers, Eloy and … eh … oh, what’s the other guy’s name. I almost can’t remember. Butragueño? Yes, I almost can’t remember him.”

The Spanish newspaper El País said, “Spain go the quarter-finals with the prestige of the man who shot Liberty Valance.” Neutrals who had fallen in love with Denmark felt as though Spain had shot Bambi. When the players returned to the hotel after the game, many of the staff were in tears. Back in Denmark, the pop star Dodo Gad wasn’t far from tears either: the defeat had cost her a trip to Mexico, as she was scheduled to sing the team song “Re-Sepp-Ten” before the quarter-final. “I was watching the games with all my friends,” she said. “‘You guys know, that if we win then I’m going to Mexico to sing.’ Everybody got really excited, and then we lost. I was very disappointed and I had to drink away my sorrows.”

She wasn’t alone in that. As they waited for the bus to Mexico City the following day, Denmark soothed weary limbs by drinking orange juice with champagne. It was somewhere between a party and a wake. In Tipsbladet, Per Høyer Hansen wrote that Jesper Olsen played “Re-Sepp-Ten” on repeat on a ghettoblaster and made a speech to the hotel manager before giving him the ghettoblaster as a present. Ivan Nielsen, the only man with Danish cigarettes, sat puffing away on the quiet table. Lerby’s son Kaj christened Olsen Jesper Julemand (Jesper Santa Claus). The hotel staff sang Viva Dinamarca as the players set off.

“I was drunk for four days,” said Nielsen. “We were up the whole night. The next day we went on the bus to Mexico City. We filled the bus with beers from Carlsberg and were singing “Re- Sepp-Ten”. Then we got there, we went to a nightclub, and the day after we took the plane. We had a few drinks during the flight. Look at the pictures when we come back to Copenhagen, we are all wearing sunglasses. We hadn’t slept for three days.”

The players returned as heroes, but a defeat so shocking demanded an explanation, both in Denmark and around the world. Victory has a thousand fathers but defeat is an orphan. In the immediate aftermath the majority went for the obvious: Olsen’s backpass, even if the tape told a different tale, that Denmark were much the better side at the start of the second half.

There was no particular backlash against Olsen, no effigies or hate mail, but it did define his memory. The backpass has cast a shadow over an outstanding career. “Youngsters only see YouTube,” said Michael Laudrup. “If they hear the name Jesper Olsen they only think of the backpass. If there’s a player who deserves much more credit for what he did for Danish football, it’s Jesper Olsen.”

Many footballers have had moves named after them: the Cruyff turn, the Panenka penalty. Not so many have had a description that extends into popular culture. A rigtig Jesper Olsen (a real Jesper Olsen) is used in Denmark to describe a mistake in any walk of life − even in politics. At a conference of the Social-Liberal party in 2001, the term was bandied about to chastise a former leader who publicly criticised the incumbent.

“If we won 3-1 then nobody would have really said anything,” said Olsen. “It was emphasised because we lost 5-1 and their way back into that game was that goal from Butragueño. It depends: where do you look in a game, where did it change? I suppose that was probably the moment, even though you can regroup.”

To many, Olsen book-ended the era of Danish Dynamite with his glorious solo goal against England in 1982 and his backpass against Spain four years later. He eventually moved to Australia. “It doesn’t bother me now, but obviously it did for a while,” said Olsen. “Not living in Denmark was probably a good thing because it was one of those things where you think, ‘Oh, bloody hell…’ I also think I learned a lot from it about how to deal with stuff. It was very good personally to have to get through that, and with people too. I never heard anything really bad said but it was a real process to get through.”

There was far more to Denmark’s defeat than a bad backpass from Jesper Olsen. Even Diego Maradona had a theory; in his autobiography he said, “the manager went mad.” Three decades later there is no shared discourse. Those involved cite various factors: the Danish mentality, the training, the heat, the tactical naivety, the absence of Arnesen, the substitution of Eriksen for Andersen. The truth, as ever, is somewhere in the middle. “If Danish players thought they needed a holiday or if it was being dragged out too long for some, then that has something to do with the mentality,” said Piontek. “I don’t think we trained too hard. We were in top shape. You don’t win 6-1 against Uruguay if you are not in shape. We had energy left in the first half against Spain. Of course when you concede a stupid goal like the one Jesper Olsen did then you lose some of the atmosphere and it can seem a bit depressing.”

Gehrs has a similar view. “I had expected much clearer disappointment from the players than I saw. I think that somehow they thought they had done what everybody could expect of them by winning the Group of Death and playing the best football of the tournament. As Sepp used to say, that was the old Danish mentality coming to the surface.”

Most of the players reject the notion that they had the keys to the kingdom and a subconscious that told them they were trespassing. “Most of this discussion came after the match, because we had a big party,” said Berggreen. “It wasn’t because we were happy. After being in a training camp for two months you start to have some alcohol and you get drunk very, very easily. Two beers and you are starting with the jokes. So we looked happy, and that went into Sepp’s head: ‘Ah, they are not so unhappy at being knocked out.’

“We were totally finished physically, there was nothing more in us. Also because of the concentration, you have to be focused, it’s very hard. You play at midday, running like crazy and fighting like crazy. It was total soccer, something totally new, a fantastic level, but you can only play it when you are running twice as much as the other teams. There was no more in us. We were kaput.”

It was difficult for Denmark to stop themselves on the field when their natural instinct was to attack with abandon. That approach went too far as soon as they fell behind to Spain. “It still hurts me that we lost,” said Laudrup. “Not because it was 5-1, but because it was stupid to lose the way we did. I think it was a lack of experience in this kind of competition.” In a post-mortem in the Observer, Hugh McIlvanney slammed their performance with liberal use of a word that was no longer supposed to apply to Danish football. “Denmark’s swashbuckling marauders lost a stunningly amateur equaliser to Spain and continued to perform so amateurishly thereafter that the intelligently deployed, hungrily competitive Spaniards buried them like paupers.”

Even though they went out in the last sixteen − the same as entirely forgettable sides from Italy, Morocco, Paraguay, Bulgaria, Poland and Uruguay − they are forever associated with the tournament. Only the winners, Argentina, left a more indelible impression on Mexico 86. Fifa’s technical report of that World Cup said they “played the most spectacular football during the tournament … their readiness to risk something, linked to a full physical commitment, provided the Danish game with an exceptional dynamism.”

In a strange way, Denmark went out on their terms. “We showed that football can be played in a way which is fun, but which ultimately is not always effective,” said Piontek. “We gave European football a new dimension and that’s some consolation.”

In the next round they would have played Belgium, then Argentina, then West Germany in the final. Could they have won the tournament?

“Noooo,” said Laudrup. “Winning competitions is not only about quality. It’s about experience. There is a reason the big teams always go on to the quarter- and semi-finals. We had the quality to go far − I think we had more quality than Spain and Belgium − but we would have played Maradona in the semi-final and we would have lost to him, like everybody did.”

Bertelsen offers a different view. “Both in France and in Mexico the championship was within reach. We could have been European champions, we could have been,” − he exhaled, almost unable to say the words − “world champions.”