The Wald Hotel is set in the hills above Stuttgart and encourages ‘forest bathing’ – periods of mindfulness in the surrounding Degerloch forest. It’s the only form of elevation the Switzerland team, who have made it their Euros base, are seeking at these championships.

There is a distinctly low-key and understated air about England’s quarter-final opponents. They train at an old, rather careworn local suburban football stadium in Waldau, carpeted with stickers and graffiti by fans of the regional Stuttgart Kickers team, who use it. The backdrop is the city’s TV tower, the first of its kind in the world to be constructed from reinforced concrete. It’s certainly not paradise, though it is within walking distance from the Wald. The team sometimes take that walk.

They stage press conferences before the sun’s barely up – 9.30am sharp, with Swiss precision timing. The silence outside is broken only by stadium staff turning leaf-blowers on training pitches, where there appear to be no leaves, and children arriving at a local school. Back at the Wald, the team play Uno, black jack poker, a card game the Swiss call ‘brandy dog’, table tennis and darts. There are no social media posts. They want to exude an understated air of calm.

Easier said than done – because the Swiss nation’s reputation for neutrality and dependability belies the fact that they usually have one tournament controversy in them. They’ll be drawn against Serbia, a fixture with a nationalist edge, where all hell lets loose. They’ll exit badly, with knockout defeats by Spain and Portugal at their last two tournaments. Or Xhaka, traditionally not one to keep himself to himself, will court publicity.

In 2021, he visited a tattoo studio before the Euros – in the face of Covid restrictions, then dyed his hair blond. Not a good look before the 3-0 last-eight defeat to Italy which was one of their worst performances in a decade. At the last World Cup, ‘Nati’ – as the national squad are known – were hit by a virus.

Their coach, Murat Yakin, this week said he empathised with Gareth Southgate and his troubles. ‘I can put myself in his shoes. I experienced something similar last year,’ he said this week, referencing a grim run of results, compounded by the 2-2 at lowly Kosovo which led Xhaka to publicly criticise him. In their last seven qualifiers of a weak group, Switzerland only beat Andorra.

Yakin wasn’t sacked, despite public clamour, but that crisis was a turning point, leading him to make three flights to Germany in February and March to see Xhaka, who has been reinvigorated by Xabi Alonso at Bayer Leverkusen. Over a few glasses of red wine in Dusseldorf, a truce was struck, with Xhaka seemingly persuading Yakin to switch to the three-man defence which has served Leverkusen very well. Xhaka felt it was better suited to the nation’s players. Yakin has even been building bridges with Ragip Xhaka, the captain’s father.

No-one knew for sure whether the new system would work out here but, as Switzerland’s Blick newspaper has put it, ‘everything Yakin touches turns to gold’ here. The team have a superb fluidity, which allowed them to get bodies into midfield and outnumber Italy. Germany struggled against them for the same reason. Michel Aebischer, the left wing back who tucks inside at No 10, epitomises it.

Yakin and Xhaka look loved up. The two of them strolled around the Waldau training pitch together for half an hour, deep in conversation, after the 1-1 group stage draw against Germany. Xhaka was in trainers and casual gear. ‘It seems as if they are one heart and one soul,’ Blick observed.

It is the new assistant manager the Swiss federation have put in place who has really changed the mood around the camp. Out went the previous assistant Vincent Cavin, a video analyst who had worked his way up the pecking order. In came 50-year-old Giorgio Contini, an established, multi-lingual club manager who has worked as Yakin’s assistant before. He’s strong on communication, talking to players about their children and their lives, and he leads the training sessions while Yakin looks on. ‘The player-whisperer’, they call him in Switzerland.

Yakin has been looking beyond football for sources of inspiration, too. He brought in Swiss Olympic ski slalom champion Marco Odermatt before one of the warm-up games against Estonia. Odermatt even stood next to Yakin as they sang the anthems, in the game Switzerland won 4-0.

There is a Swiss unity here borne of so many of this squad having played together for so long, with four players around the 100-cap mark. That nucleus won the 2009 under-17s World Cup together in Nigeria. This is certainly a more experienced side than England. It’s a collective, too. No team at these Euros has more goalscorers than their seven.

But behind the calm, benign exterior, Switzerland are afflicted by an unmistakable pressure created by ten years of knock-out stages. There is a sense in the nation of nine million people that the team must now rid itself of the notion that there is honour in elimination at this stage. If Switzerland do not take the next step to a first ever tournament semi-final against a wounded, struggling England team, the logic runs, then when will they?

‘There is a wish – a need – to draw on the inspiration of Roger Federer,’ said one source. ‘He never settled for quarter-finals.’

Switzerland’s AEK Athens winger Steven Zuber, twice on the losing side against England in the past few years, said of his country on Thursday: ‘We are a nation that has set ourselves limits, told ourselves that we are not allowed to go further. I hope that is gone now.’ Midfielder Remo Freuler said earlier this week: ‘It’s more the media that always talk about the “little Switzerland”. But in terms of football, I believe we have earned a lot of respect in recent years.’

The team were joined by their wives and girlfriends to celebrate the Italy with pizza, leading some of the Swiss media to contemplate whether it will be ‘fish and chips’ for them on Saturday night. Switzerland can scarcely believe its team are considered favourites. ‘Somehow the football world has gone off the rails when English journalists unanimously identify Switzerland as the favourites against the Three Lions,’ Blik reflected.

There is a concern that if Xhaka’s influence is choked off, then Switzerland may not be the same team and that Scotland’s Scott McTominay was successful when assigned that detail in the group stage game, a 1-1 draw in Cologne. It is lost on no-one that England’s Kobbie Mainoo could be asked to perform a similar role against Xhaka when the Swiss face their latest British opponents.

Yakin can hardly believe the way the national mood in Switzerland has swung his way. In the press conference after the Scotland game he was even asked how it felt to be ‘a sex symbol.’ He responded to say that he hoped his wife wasn’t listening.

His own choice of recreation at the Wald Hotel is chess, rather than poker. ‘A chess piece has no emotions, so you can’t compare players and pieces,’ he said of his love of the game, before the tournament. Eventually, he and his team will have to emerge from their quiet reverie in the hills. They’re holding out for as long as they can.