The red and white train just keeps rolling along. In the city where Russia’s space programme shot for the moon, England’s footballers have now entered their own near-earth orbit. There they go now, a little giddy but still upright, out there floating in their tin can, high above the world.

It has been a month and a day in Russia, all the way from the fly pits of Volgograd, to Kaliningrad on the Baltic, and now on to Samara, a city lodged in the humid armpit of the south-east. But after Wembley in ’66 and Turin more than a quarter of a century ago, a 2-0 defeat of Sweden means England will now decamp to the Luzhniki Stadium in Moscow to play Croatia for a place in a World Cup final.

Before then there is time to take a breath and drink it all in. Because these are also the moments that imprint themselves and remain intact, that moth-eaten brocade of stories and heroes that sport likes to save to the deep hard drive.

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Did you see the England fans? They came by rail and minibus, with nowhere to stay, with rooms scrounged and airport benches staked out – and with a Gareth Southgate impersonator in their mix too, in full waistcoat and Gareth ’do, high-fived and hugged as they bounced and gurgled and sang the same old songs all over again.

Did you see Jordan Pickford flying like a tumbler, punching the air with pre-celebration at each fine save? Did you see the players at the end, caught in wide-screen close‑up, faces glowing with a rare kind of joy? This is a team that has simply been allowed to show its best side, and which has somehow evaded that entitled glower of some more illustrious predecessors.

There was Kyle Walker clapping and laughing and doing silly dances. And Harry Maguire who has the air of a man who might turn up to a training camp carrying his belongings in a bin bag, if only because he did once turn up to a training camp carrying his belongings in a bin bag.

Facebook Twitter Pinterest England’s unexpected run to the semi-finals has led to joyous scenes back home, like this one on Brighton beach. Photograph: Gareth Fuller/PA

Did you see the curves of the Samara Arena, a sleek new stadium with a pronounced resemblance to the Millennium Dome – albeit more an evil Millennium Dome, the one that will later hatch into an alien egg? This is one of ours now, a stadium that will, like it or not, enter England tournament lore.

There were two things worth saying about England’s performance. First, the set‑piece mastery continues. Ashley Young’s routine is pretty easy to read now, although doing anything about it is a different story. He has an excellent technique, using the top of his foot to send the ball in a hard, flat, dipping arc.

In the first half the ball found Maguire, leaping forward and thunking it out of the sweet spot down and into the corner. When Maguire heads it like that you feel there should be a suitable audio effect superimposed, the sound of a large Victorian wardrobe falling over or a mortar gun pounding the cliffs at Iwo Jima.

England were organised, smart and unified. But they were actually good, too

It was also a beautiful two‑touch goal, so ludicrously sweet and pared back it resembled the kind of goal you might score a hundred times a day in a 20-year-old computer game.

Sensible Soccer: this is what England have played in Russia, a world where if you press B and hold down A, then waggle your stick at just the right moment the same thing just keeps on happening over and over again.

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Can they upgrade the features from here, make it more intuitive? This is the second thing about England. We knew they were organised and smart and unified. But they were actually good, too.

Not at first. The game started scrappily. But 10 minutes after half‑time England were suddenly all over Sweden, pulling them from side to side and combining with real urgency. It isn’t fanciful to suggest they had a bit of Manchester City’s about them in those best moments, moving the ball wide, looking for overloads, ready to switch it if the space opens.

This is where Dele Alli’s goal came from, Young pulled out wide on the left repeatedly, Sweden’s defence quivering and groaning at its limits like a world’s strongest man contestant about to drop his sack of flour. The ball was switched, Lingard crossed, Alli headed in. It will do him a great deal of good.

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A last word on Gareth – yes, just Gareth – also known as Gal and Sir Nord of the Order of the Waistcoat, who has begun to radiate a kind sporting ur-power, that luminous authority of a coach in his sweetest moment, entirely in control of the elements around him.

Taking England this far is an admirable achievement for a man who despite his lack of experience has shown a ruthless will and a forensic ability to work the smallest details.

Sport can change so quickly. But right now there is a fair case that, judged on grams of talent versus heights reached, Southgate has done as much in the job as any of his predecessors.

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His triumph has been to create that rarest of things with England, an actual team culture. And while England have faced opponents of lower quality in Russia than those in the knockout stage of Italia 90, there is also no Charlton or Gascoigne in this team and no home advantage.

Whatever happens from here we will always have the pleasure of watching this process develop, the decency of Southgate’s motives and his ideals on how his team should prepare and present themselves. It has been surprising at first, then admirable, then encouraging. For the first time in Samara it just felt like a blast.