What great players do in England or against English teams matters – in England and most probably across the UK.

Perhaps less so than before YouTube took highlights from Brazil to Blairgowrie in the blink of an eye, but still. It is the reason why Lionel Messi was asked, before the 2011 Champions League final at Wembley, about the fact that he had never scored on English soil. As if he had not yet arrived.

That is one reason why Zlatan Ibrahimovic was being reassessed after his demolition of the England defence on Wednesday night.

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This trumped the Swede's previous best in this strange sphere of influence, his lead performance in AC Milan's 4-0 rout of Arsenal in February. He played immensely that night, assisting in two goals and scoring a penalty after he was fouled, but it was in Italy, for an excellent Milan team and against a comparatively weak Arsenal side.

In the build up to the England game, Ibrahimovic had indulged questions about Steven Gerrard, who celebrated his 100th cap in the friendly. He should play in a foreign league, said Zlatan, who has won the Eredivisie with Ajax, La Liga with Barcelona and Serie A with three clubs, before his two titles with Juventus were rubbed from the records. He was not without praise for the Liverpool captain, however: "He has a big heart, always fighting." Unsaid: Not like me.

Gerrard described the final of Ibrahimovic's quartet of goals as the best he had seen. It was a marvel of the imagination as much as of athleticism. It is conceived even as it becomes clear that Joe Hart, the England goalkeeper, will reach a bouncing ball before Ibrahimovic and the striker begins his retreat to where he assesses Hart's header will go. He is 6ft 5in tall but achieves such height and rotation in executing a bicycle kick that he lands on his shoulder, not his backside. For the UK-based doubters of a talent unique in the game, there was nowhere left to go.

The trouble with Zlatan has never been his ability. It was all the other stuff.

The league titles and the accumulative transfer fees (at 30 he has cost a total of £150m, making him the world's most expensive footballer) put Ibrahimovic at the top of the market in international football. He is a premium product ahead, in all measurable industry terms, of Wayne Rooney at Manchester United, Sergio Aguero across town at City and Fernando Torres at Chelsea. His showreel contains some incredible goals: dribbles, long-range shots, volleys, free-kicks and one 22-yard bicycle kick. What's not to love?

Well, quite a lot. Ibrahimovic has always operated on his own terms. He has a history of violence and is a black belt in taekwondo. He reportedly put this training to use on Milan team-mates Antonio Cassano and Rodney Strasser.

He was tainted in the eyes of many observers by his time at Barcelona. He cost the Catalans €48.5m in cash, plus Samuel Eto'o, and signed a €75m contract. He was sold to Milan for €24m a year later after the disintegration of his relationship with the manager, Pep Guardiola. In his explosive autobiography, which sold in Sweden faster than Dan Brown, JK Rowling or Stieg Larsson, he detailed the primary reason as an unwillingness to be instructed in Guardiola's delicate tactical construction, the basis of which was to get the ball to Messi where he could damage opponents. "I have always liked those who drove through red lights," was how the Swede put his attitude.

He has had frequent run-ins with the media. At Barcelona, images of the striker with his team-mate, Gerard Pique, outside the stadium provoked sub-tabloid chatter about a homosexual relationship between the pair. Questioned on this by a female television reporter the next day, Ibrahimovic invited his inquisitor to follow him home so he could demonstrate his prowess.

Ibrahimovic is a rebellious footballer. He plays with his chest out. He confronts opponents, team-mates, managers and media. He struggles to play second fiddle to anybody, but given the role of virtuoso he can hit notes that only a handful of forwards in the world can match. In all of this, he is reminiscent of nobody so much as Eric Cantona, the one-time enfant terrible who is now remembered as an icon of the English Premier League.

Unlike Cantona, Ibrahimovic's temperament has not cost him an international career. Although he has never dominated a tournament, his strike rate of a little under a goal every two games in a Sweden team of oscillating fortunes does not talk of an unreliable talent. He has won more than Cantona did.

In the final analysis, perhaps most of us in the UK, and those in England in particular, only really believe what we see. Thierry Henry is undoubtedly held in greater esteem here than he would have been had he succeeded in Italy and not been sold to Arsenal. Our understanding of the ferocious talents of George Weah and Andriy Shevchenko, untouchable at Milan, is damaged by their paycheck performances for Chelsea after they had lost top gear. And Ibrahimovic is no Cantona, simply because he didn't do those same things in Manchester, London or Liverpool.