Alexander-Arnold, dropped from the starting team after two disappointing performances in the group stage, came on as a late extra-time substitute to take the glory after Jordan Pickford had saved Switzerland's first spot-kick from Manuel Akanji.

It was the third successive UEFA Euro 2024 quarter-final to go to extra-time, two of them to penalties.

Breel Embolo had put Switzerland ahead after 75 minutes, with Bukayo Saka levelling five minutes later in a game of few chances.

Saka, who missed in England's UEFA Euro 2020 final shootout defeat by Italy, stood up again here and converted in front of a wall of England fans, putting a huge smile on the Arsenal man's face.

"He is so brave, he's one of our best so we were never in any question that he was going to take one," coach Gareth Southgate said of his midfielder.

Saka said: "To come back from something like that was really difficult. I used that to make me stronger. Today I took the chance and I'm happy.

"Hopefully next game we can win in the 90 minutes but if this is what it takes, we'll do anything."

That next game is Thursday's (AEST) semi-final in Dortmund against Netherlands, and while England will almost certainly have to find more intensity and accuracy in attack than it showed against Switzerland, the confidence gained from another shootout win after decades of pain will be priceless.

"Incredible," Alexander-Arnold said. "These are the goals and aims that we set for ourselves. The team showed a lot of character, belief, a lot of heart and spirit out there. We dug deep when it mattered most.

"A lot of practice goes into that moment," he added of the penalty he smashed into the top corner. "I practice. I knew what spot. I knew I just needed to execute it and I went out and did that."

England came into the game on the back of two dire performances and although it showed more invention and movement there was again little end product, and with the Swiss equally cautious, there was barely a meaningful effort on goal for an hour.

Switzerland, an impressive victor over Italy last week and seeking its first major semi-final, took the lead after 75 minutes when Dan Ndoye whipped in a deflected low cross from the right, with Breel Embolo stretching in front of Kyle Walker to poke it home.

Southgate responded by immediately throwing on three substitutes – Cole Palmer, Luke Shaw and Eberechi Eze – and five minutes later England was level as Saka cut in from the right wing and curled home a brilliant 20-metre left-footed shot that went in off the far post.

In extra-time England's Declan Rice had a fizzing shot from the edge of the box brilliantly saved by a diving Yann Sommer, while Xherdan Shaqiri clipped a post direct from a corner, before the penalties that had felt inevitable almost from the start duly arrived.

Switzerland had lost three of its four major tournament shootouts, while England’s famously uncomfortable record was seven defeats and two wins.

That reads 7-3 now after Cole Palmer, Jude Bellingham, Saka, and Ivan Toney all scored confidently ahead of Alexander-Arnold's winner.

"Huge performance, huge result for us," Southgate said.

"We had to be tactically spot on. To come from behind again and show the character and resilience that we did... winning tournaments isn't just about playing well. I thought we did play well today but you've also got to show all those other attributes to win and we showed them all tonight."

The Swiss also lost in the quarter-finals of the last European championships in a shootout, and Shaqiri said: "There is nothing more brutal than to go home after penalties.

"We fought and gave it all we had to try and qualify so that the fairytale could continue.

"We made a lot of people in Switzerland proud and gave them some joy."