At the final whistle, the victorious players converged on one another. It took a few seconds for them to gather their breath and then, finally, they could join the party that was already under way behind the goal to their right. England had booked their place in a World Cup semi-final and this kind of euphoria has been so long coming – more than a quarter of a century since the last occasion – it was probably just inevitable they would soon be dancing on the pitch as well as in the stands.

If we were to be picky, a legitimate argument could be made that England will need to play with more finesse if they are to harbour serious ambitions of winning this competition. They will have to pass the ball more efficiently and maybe, in possession, show a touch more arrogance, in the manner of a side that really believes they are the elite and this is where they belong. France, for example. Or Belgium.

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For now, however, Gareth Southgate and his players are fully entitled to cherish these moments bearing in mind the last time it happened Bobby Robson was manager and Spitting Image’s puppet of the England coach was a senile worrier called Rubbisho. Turin, 1990, with the penalties, Gazza’s tears and all that, is written into England’s history. This time, maybe there will be a happier ending. But the real glory will only be attainable in Moscow next Sunday and, on this evidence, they should not hold any fears about meeting Croatia in Wednesday’s semi-final.

Why not be confident, after all, when England have now scored as many goals, 11, as Sir Alf Ramsey’s side in 1966? Eight of them, astonishingly, have come from set plays, the latest being the header from Harry Maguire to swing this game in England’s favour. Some might even argue they are too reliant on scoring this way. For that, show them the tape of Dele Alli’s goal or the other occasions when they threatened to add others.

England played stodgily at times, particularly in the first half, but it was a controlled performance overall and, importantly, the four players who would have missed the semi-final had they received another booking remained out of the referee’s notebook. Southgate’s team will be at full strength on Wednesday. Anything, as he says, is possible.

Facebook Twitter Pinterest Dele Alli scores England’s second goal in their World Cup quarter-final victory against Sweden at the Samara Arena. Photograph: Kieran McManus/BPI/Rex/Shutterstock

At this point, as is becoming the norm, it is probably worth noting the now-familiar reminder from England’s manager that it is still not time to get too carried away. Not yet, anyway. Equally, Southgate also made the point that his team can play considerably better than they did for long spells of their latest victory. Early on it was disconcerting to see the way his team struggled, the way passes were misplaced and the suspicion, however briefly it passed, that the occasion had got to a couple of his players.

In their previous matches, England had been so quick to set the tempo, passing the ball incisively and making it clear very quickly that they would be happy to take the game to their opponents. That was not the case here. Ultimately, though, that sluggish start will quickly be forgotten and once they had taken the lead, half an hour in, there were only fleeting moments when England looked in any danger.

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Until that point, it had been a laboured performance. But then England won their first corner. No other player in the World Cup has won more aerial challenges than Maguire and it was strange, to say the least, that Sweden had designated Emil Forsberg to mark him. Maguire had a seven-inch advantage and made it count. It was a mismatch, the ball thudded off Maguire’s forehead, powered in to the right of the Swedish goalkeeper, Robin Olsen, and England had scored from a corner for the fourth time in this tournament.

Sweden will reflect on the save that Jordan Pickford made from Marcus Berg’s header at the start of the second half and, though he was needed only sporadically, this was another splendid performance from England’s goalkeeper, showing again that he can handle the big occasion.

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Pickford pulled off another brilliant save at 2-0, when Viktor Claesson had the chance to change the complexion of the match. It was England’s first clean sheet of the tournament and there was never a concerted spell when Sweden – willing but limited opponents – managed to pin them back.

Instead, it might have been an even more straightforward victory if some of England’s better chances had fallen to Kane rather than Raheem Sterling. His first one-on-one with Olsen ended in a late offside flag, though the England player was not to know that. The second would have made it 2-0 at the interval and, though it was largely inconsequential in the end, this is the stage of the competition when Southgate desperately needs his front players to have ice in their veins. For all his many qualities, Sterling turns to slush too often and as long as that is case he will struggle to improve an England record that has now stretched to two goals from 42 appearances.

Facebook Twitter Pinterest Harry Maguire heads in England’s first-half opener. Photograph: Mike Hewitt/Fifa via Getty Images

No big deal, though. Sterling played his part, always looking to create mischief, and the way he stretches defences makes up in part for his erratic finishing. As for Kane, another goal from England’s leading scorer would have meant him outscoring Paolo Rossi when he won the Golden Boot in 1982, Gary Lineker when he did the same in 1986 and Totò Schillaci in 1990.

As it was, Kane worked hard without getting many opportunities to add to his total and, strangely, that is one of the areas where England need to improve. Penalties and corners aside, Kane’s teammates are not creating enough chances for their principal scorer.

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If that can be put right, England should be reasonably confident against anyone. For now, however, this is not a time to be too critical. Jordan Henderson had a fine match and England were largely untroubled once they had their second goal. For that one, Kieran Trippier’s pass gave Jesse Lingard the chance to clip the ball over from the right. Alli was at the far post to head the ball in and, half an hour later, the players in red were behind that goal, dancing in front of the England fans, daring to believe.