As if to sum up the weirdness of this England team stumbling into the semi-finals of Euro 2024, perhaps the only time they looked in control against Switzerland was when it went to penalties. Before then? Choked play in the final third, chaotic defending in extra time and touchline inertia were the overriding themes – or at least they would have been had another moment of individual brilliance, this time from the magnificent Bukayo Saka, not saved Gareth Southgate again.

Switzerland had England on the ropes when Breel Embolo made it 1-0 after 75 minutes. Murat Yakin’s team were dominant for much of the second half, raising the prospect of Southgate’s 100th game in charge being his last. His decisions had not worked – again. Harry Kane was off the pace – again. It was reactive from Southgate when he introduced Cole Palmer, Eberechi Eze and Luke Shaw with 12 minutes left – again.

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Logic suggests England should be out. The reality is they forced extra time when Saka, with their first shot on target, made it 1-1 out of nothing. They scrapped from there, with Shaw defiant on his first appearance in five months. Eze, out of position at left wing-back, would also impress. That said, England were hanging on at the end. Xherdan Shaqiri hit the angle of post and bar with a corner. Jordan Pickford made an excellent save from Zeki Amdouni.

England have been baffling during these Euros, with Kieran Trippier chugging away on the left and Phil Foden struggling to reproduce his club form, but here they are. For all that Southgate has seemed to be making it up as he goes along, some elements of his process-driven management remain intact. All those hours devoted to studying the psychology of penalty shootouts, of working out how to banish the demons and remove the random factor, paid off.

It was Switzerland, who have lost five of their six shootouts, who cracked; the outstanding Manuel Akanji who saw the crucial kick saved by Pickford; Southgate who keeps defying the narrative around English football.

The man who missed against Germany in Euro 96 has taken England, who have won three out of four shootouts under him, to a third tournament semi-final. Southgate has his faults, but his man-management cannot be doubted. His faith allowed Saka, denied in the shootout against Italy at Euro 2020, to have his moment of catharsis from the spot here. Belief in the collective ensured that Trent Alexander-Arnold, whose England career has never truly taken off, came on to finish Switzerland off by crashing the final penalty past Yann Sommer.

Yet England will need to be better against the Netherlands on Wednesday. They were already one lifeline down after their escape against Slovakia and there was unease at the outset at seeing Southgate unveil a rejig that still had Trippier patrolling the left flank.

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The shifts were subtle rather than revolutionary, Foden floating in an inside-right position, a compact 3-4-2-1 designed to match and stifle Switzerland. In terms of Trippier’s role, Southgate was worried about Dan Ndoye, particularly as Ezri Konsa was in for the suspended Marc Guéhi at left centre-back.

England would never look fully secure. Konsa, who did well on his sixth cap, blocked a shot from Embolo in the 25th minute. Kobbie Mainoo cut out a cross from Ndoye. John Stones halted a run from Granit Xhaka.

Many of England’s best moments came from the bright and skilful Mainoo, who always wanted the ball. Declan Rice seemed more imposing. Bellingham was more involved, one blistering run ending when Fabian Schär hauled him down.

England have improved their record in penalty shootouts at major tournaments to four wins from 11 attempts (36%) with victory over Switzerland at Euro 2024.

World Cup 1990 Semi-finals: Lost 4-3 to Germany

Euro '96 Quarter-finals: Won 4-2 against Spain

Euro '96 Semi-finals: Lost 6-5 to Germany

World Cup 1998 Last 16: Lost 6-5 to Argentina

Euro 2004 Quarter-finals: Lost 8-7 to Portugal

World Cup 2006 Quarter-finals: Lost 3-1 to Portugal

Euro 2012 Quarter-finals: Lost 4-2 to Italy

World Cup 2018 Last 16: Won 5-4 against Colombia

Nations League Third-place play-off: Beat Switzerland 6-5

Euro 2020 Final: Lost 4-3 to Italy

Euro 2024 Quarter-finals: Beat Switzerland 5-3

Saka, who had a vital role at right wing-back, had Michel Aebischer’s number. Mainoo produced a delightful turn to make space in midfield. On 44 minutes, with Aebischer beaten by Saka, Switzerland were relieved that Xhaka stopped Mainoo from converting the cutback.

England needed more quality in the final third. Their final ball lacked conviction and they made such a mess of one corner that the ball ended up with Pickford. The half ended without either goalkeeper making a save, a sign that Southgate’s tactics were neutralising not only the Swiss but also Bellingham, Foden and Kane, who had touched the ball nine times.

Switzerland, having seemed inhibited, pressed more after half-time. Embolo turned Konsa but shot straight at Pickford. Kane tried to turn Akanji, only for Switzerland’s No 5 to gently level England’s captain off the ball. All the noise came from the Swiss fans. Xhaka and Remo Freuler were bossing midfield. Switzerland still decided to tweak their approach, Silvan Widmer and Steven Zuber on for Ruben Vargas and Fabian Rieder. Aebischer volleyed over. England were penned in.

There was no response from Southgate. Switzerland’s goal duly arrived. Widmer and Zuber combined before Ndoye was allowed by Konsa to fizz in a low ball. A touch off Stones took it on and Kyle Walker lost Embolo, who slid in to beat Pickford.

Southgate reacted, Palmer, Eze and – at long last – Shaw coming on for Mainoo, Trippier and Konsa. All or nothing, Gareth. This was the cavalier England and, moments after the changes, Saka took a pass from Rice and cut inside, bending a left-footed shot through the bodies and beyond the unsighted Sommer.

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England had equalised with their first shot on target for the second consecutive game. Why are they so slow to seize the initiative? They had the team full of fun guys on now, with Eze and Saka playing as wing-backs. Embolo and Ndoye would spurn chances before extra time.

Rice stretched Sommer after the restart. Another collision with Akanji ended with Kane tumbling past Southgate and into England’s dugout, which is where he would stay. On came Ivan Toney. Eze and Palmer tried to make things happen.

Alexander-Arnold came on, then Shaqiri and Amdouni. England wanted penalties. Palmer scored his. Pickford checked his notes, delayed and dived to his left to save Akanji’s weak effort. Bellingham, Saka and Toney were nonchalant. Schär, Amdouni and Shaqiri responded, but Alexander-Arnold’s emphatic effort made it 5-3.

Sweet Caroline blared out. Southgate hugged his backroom staff and tried to make sense of it all.