They came over land and by sea, the committed and the curious, all willing England towards unfamiliar glories. And halfway through the first half – with Phil Neville’s side a goal to the good – some felt so emboldened that a time-worn shanty began to waft across the Stade Océane for the first time at this World Cup. “It’s coming home, it’s coming home,” they sang, albeit tentatively, as if shouting too loudly might awaken an old curse.

But by the hour mark, with England three up and rampant, there was no holding back. The same words were chanted, only this time with far greater intensity and belief. Now all roads lead to Lyon, and a semi-final with France or the USA, and the bandwagon will only grow.

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Perhaps it will end in tears. It usually does with England. But any exit is unlikely to be acrimonious. Indeed, walking through Le Havre it was noticeable how normal the atmosphere was, with fans quietly having a beer, mixing with locals, or doing their own thing. This is not a familiar sight to watchers of the men’s team, who retain an element of support that regards itself as an invading army. Its modus operandi is a familiar one: mark territory with St George’s cross flags and the consequences of an overworked bladder, drunkenly taunt police and passersby, and chant sepia-tinged songs about bygone days.

There was none of that here, inside or outside the stadium; if this was a cinema screening it would have carried a U-certificate. Steven and Carol Hibbs, who had travelled by motorhome from Staffordshire to watch England in the knockout stages, said they were struck by the different atmosphere between watching the men’s and women’s teams play in foreign tournaments. “There’s no raucous fans and it is definitely more family orientated,” said Steven. “I’ve seen a lot of women supporters out together in groups.”

Facebook Twitter Pinterest David Beckham was in attendance with his daughter and gave the England team a pep talk before the match. Photograph: Loïc Venance/AFP/Getty Images

Ten German bombers? In Le Havre it was closer to lo-fi love bombing – with fans displaying a gentler English patriotism without the snarl or superiority complex.

Many of these supporters had arrived in France on overnight ferries, some converted to the women’s game by the saturation of coverage and the growing sense that Neville’s side might – despite their occasional moments of complacency and drift – have enough about them to make history. A few admitted to having barely slept. You got the sense they wouldn’t on this night, either.

Emma McIntosh, who had travelled with four friends from Newcastle and caught the overnight boat from Newhaven, was more succinct. “Less alcohol and more culture,” she said, summing up the differences between men’s and women’s supporters. “And everybody gets on with everybody. It’s the summer of women’s sport, with the football and netball World Cups, and I really think it could be a turning point for how we are treated.”

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There was another thing McIntosh noticed, too. The number of new fans. “We were also here for England’s match against Argentina – that was a midweek game but there were about 15 under-11 kids with their parents cheering England on,” she said. “It was unreal. We also spoke to three lads earlier who had driven down from Manchester to watch the game purely because they had got into women’s football at this World Cup – and I am sure they are not the only ones.”

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Among their number was David Beckham with his daughter Harper, the stadium camera capturing every shared moment of glee. Dozens of other parents would have enjoyed a similar, if infinitely more private experience.

Meanwhile McIntosh’s friend Claire Uttley, a former player for Doncaster Rovers Belles and England Women, was thrilled by how much had changed since she had started in the 1980s. “When I was seven I played for the local boys team but when I got to 11 or 12 I was told I couldn’t play with them any more so I had to get a train and then a bus to go training with a women’s side,” she said. “We then had to pay to play, to travel and for our kit.”

Uttley, 40, who played five times for England, said that things had barely improved towards the end of her career. “I was lucky to get travel and expenses for most of my career – I think the most I was ever paid was £50 a game. So it’s wonderful how much the nation is getting behind this team. That said, I do wonder how many people will maintain their interest when the Women’s Super League kicks off.”

For now, though, most English minds are merely on Lyon, where Neville’s side play their semi-final on Tuesday. The team will be underdogs, whether it is France or the US lined up against them. But after this performance, who can blame them for believing they can prolong the hope – and the giddiness.