It was only as England’s two buses departed the Stadio Olimpico at around 12.45am yesterday morning that Gareth Southgate got to scroll through the many, many messages of congratulations on his phone. The majority received a lot of gratitude in response, but also the same three words back.

“On to Wednesday.”

The mood was that bit different from England’s last quarter-final victory, against Sweden in the 2018 World Cup. There was satisfaction and celebration in Rome, yes, but it was no great sensation. No one was describing it as an unbelievable feeling this time.

This is something else that has already changed about this squad.

If there is still a big question over whether this group can be champions, they are now undeniably a tournament team. They are attuned to the rhythm of these events. Latter-stage knock-out games no longer hold any sense of awe.

“The interesting part for us is we won’t feel totally satisfied if it’s just a semi-final, whereas maybe three years ago – although there was massive disappointment after the semi-final – there was a feeling we’d come a long way,” Southgate said. “Now we’ve replicated what we did there, but that won’t be enough to fulfil the group.”

Even that evolution in thinking is important, but it comes from hard experience. Much has been made of how Southgate and his staff conducted detailed studies into what wins tournaments, but there’s a difference between knowing the path and living it.

It is why the core of the team, those players with the longest England careers, have been so important. For all the focus on the youth of the squad, it could even be said that the 4-0 victory over Ukraine was mostly a victory for those senior players, who have actually faced the most questions of late.

Part of the reason it was the perfect win was because of so many previous imperfections, and how smoothed they were.

Consider Southgate’s core leadership group. Jordan Pickford has had a difficult time at his club, and there have been frequent calls to drop him. He made a crucial save early on here, and underpinned a defence that kept a record fifth consecutive clean sheet at a European Championships.

In front of him, Harry Maguire started the season with a Greek court case hanging over him and ended it injured, with frequent questions over whether he should be in the squad. He instead complemented another clean sheet with a first goal of the tourmament.

“The beginning of this season was very difficult for Harry on a number of fronts, so it’s brilliant to see how he has emerged with so much more confidence as a leader,” Southgate said. “You can see he’s more confident in himself and has gone on to another level, not just on his game but on his maturity.”

Raheem Sterling has faced similar questions, and has even spoken of his unhappiness at the lack of football with Manchester City. He has responded with a series of performances that make him a contender for player of the tournament, on Saturday adding a supreme assist to his array of goals.

Sterling supplied a player who he had covered for in the opening games, with Harry Kane’s lack of goals leading to debate over whether he should be dropped. The striker has settled such discussion with three knock-out goals, as he now looks like he could again be a tournament top scorer.

“We said after the goal against Germany that could be a massive release,” Southgate said. “I think we saw that with the finishes against Ukraine and then the incredible volley just before the corner for Hendo’s goal.”

That header that completed the rout might actually be the most significant strike of the lot, and not only because it was Jordan Henderson’s long-awaited first international goal. The reaction displayed the collectivism of the squad.  

“I loved some of the reaction on the bench when Hendo scored because you could see the younger players were totally delighted for him. There’s a lovely moment with Jude that shows you what Hendo brings to our environment, that the players were so pleased for him. We all were.

“He’s really accepted that this was going to be a difficult and different challenge but he’s totally thrown himself into it. When I talked to him a few weeks ahead of the first training camp we talked through this scenario, he was adamant he just wanted to be a part of it and wanted to contribute in any way he could. It’s brilliant for him that he’s had a moment like last night and he’s been crucial around the camp as to what we’re doing.”

This is precisely the point about that core, and what they carry through. Southgate refers to them as the “tribal elders”.

“Within in any team there’s a core group that drive the team and I don’t think you can underestimate the importance of that, I’ve talked before young players that have high ambition and they want to win and they want to do well, but there’s a bond between groups that forms over a period of time where you know when challenges are made, when there’s a need to dig in, when things are happening around the camp and that core group is really important.

“The lads that were with us in Russia, the lads you just mentioned, (Kieran) Trippier is another one, Pickford another one, they’ve been through these experiences together that they pass on to the younger group as well and the newer group and they take the lead from the tribal elders, if you like, so I think it is key. It’s not just about talent.”

England’s clear expectation is to get into a final. A semi-final no longer cuts it.

“We’ve knocked off so many hoodoos or perceived barriers already and I feel like this group of players will feel this is just the next challenge,” Southgate says.

“Our group are ready to get to the next step – they are excited by that challenge.”

They are now, undeniably, a tournament team.