People often talk about jumping for joy but it is relatively unusual to see a full-grown adult actually do it. Such scarcity value meant things felt significant when, late on Sunday night at a small, slightly dilapidated, football stadium in the ancient Netherlands city of Deventer, a 34-year-old Welshman offered a perfect physical demonstration of such rare, unbridled happiness.

Like many football coaches Mark Sampson quite often waves his arms around and punches the air with excitement but no one had previously seen England’s manager dash on to the pitch and launch himself off the ground in quite such dramatic fashion as he did at the final whistle against France.

It was a giant, twisting leap, concluding with Sampson remembering his etiquette and racing back to the touchline to hug his losing France counterpart, Olivier Echouafni. The entire, rather touching, cameo seemed thoroughly emblematic of the great stride forward the Lionesses had just made.

Thanks to Jodie Taylor’s second-half, Euro 2017 quarter-final goal England had beaten Les Bleues for the first time since 1974 – and at the sixth attempt under Sampson. The 1-0 win propelled them into a semi-final against Holland here on Thursday night and earned their young coach comparisons to Sir Alf Ramsey.

If Sampson, who choreographed England to third place in the World Cup in Canada in 2015, can conjure two more victories, his Lionesses will become the first senior England football team to win a major tournament since Ramsey’s World Cup class of 1966.

As the familiar strains of “Three Lions” and those haunting lyrics about all those “years of hurt” and “never stopped me dreaming” echoed from the slightly tinny stadium sound system, success here certainly seemed within tantalising touching distance.

The Football Association has poured considerable effort, enterprise and cash into women’s football in England over the past few years. Its £17.7m annual spend on the sport is Europe’s highest and a trophy would represent a tangible justification of such investment.

It would also serve as an important stepping stone towards fulfilling Sampson’s ambitious goal of building “the best team on the planet”, involving his side – fifth in the international rankings – replacing the United States as world champions in two years’ time.

More immediately England may never have a better chance of winning their first women’s football tournament. Also on Sunday Germany, the European Championship holders who had lifted the trophy six times in a row, were shock quarter-final losers to Denmark while unfancied Austria beat Spain.

Sarina Wiegman’s fast-improving Holland side should not be underestimated but Sampson’s players, after winning all four of their games here, scoring 11 goals and conceding one in the process, are suitably confident.

“We’ve always said we really believe we can win this tournament – and that’s a big thing to say from the start,” said Jill Scott, a key midfielder who is suspended on Thursday but “very much available” on Sunday when Enschede hosts the final.

“Playing France I just knew that we weren’t going home. I didn’t even think about us not getting through. We all really believe we can win this tournament and it shows. People are putting their bodies on the line.”

Scott feels she and her team-mates are endeavouring to lift the trophy not just for themselves but for those pioneering international predecessors who helped pave the pathway towards these moments in the Netherlands sun.

“I wouldn’t say we’re the best England team ever,” said the Manchester City player. “We’re part of a project that’s spanned many years. We’re all full-time professionals now and we’ve got a lot of resources but that’s down to a lot of the work that Hope Powell [Sampson’s predecessor] put in over 15 years, during the time we were part-time and didn’t have the resources. If we were to lift the trophy on Sunday, it would be for every player that’s pulled on an England shirt over I don’t know how many years.”

Sampson has divided opinion with a sometimes provocative public persona – he called Echouafni “wet behind the ears” and decried Spain’s “dark arts” – yet this confrontational demeanour is perhaps more about the pressure the former Swansea City academy coach is facing rather than a lack of humility or humour.

In private Sampson is considerably more nuanced than some of his comments might suggest. “Mark’s very honest,” said Scott. “He’s definitely a people person. He’s put in such a lot of work on and off the pitch with us; I think that’s why we’ve got this belief and real togetherness. Mark’s doing a fantastic job. In the past, whenever you did interviews, you always said: ‘Yes, we’re together as a team,’ but here it really feels natural.”

A disciple of the “devil in the detail” school of coaching, the former semi-professional defender has persuaded the FA to fund the installation of a costly gym at England’s Utrecht base as well as the expensive rental of a restorative cryotherapy chamber. Less extravagantly, colouring books and crayons are among assorted relaxation aids available to players during downtime.

If England are still not quite Europe’s best technically, they are formidably strong in terms of tactics, physical fitness, psychology and emotional control.

Some opponents are rather jealous of the Lionesses’ five-star pampering but relations remain generally good with a Holland squad containing six England-domiciled players, earning their living in the Women’s Super League.

“We know a lot of the Dutch from the WSL,” said the goalkeeper Siobhan Chamberlain, who replaced the injured Karen Bardsley during the France game and is likely to start on Thursday.

Chamberlain trains against her Liverpool colleague Shanice van der Sanden, and Jodie Taylor – England’s star striker and Euro 2017’s leading scorer with five goals – does likewise with the Dutch keeper Sari van Veenendaal at Arsenal. “Shanice and I have been texting each other congratulations but we’ve now said: ‘The good luck wishes stop here,’” said Chamberlain. “We’ve come to this tournament to win it.”