Two days before the start of the Euro 2020 football tournament UK prime minister Boris Johnson told the House of Commons he wished “all the very best to Scotland and England and all the home nations that may be playing”.

His failure to name Wales — a nation of just 3.2m people that reached the semi-finals of the last Euros in 2016 — prompted a short tweet from the Football Association of Wales. “And Cymru?!” it asked, using the Welsh language name for the nation.

The UK fields four separate international football teams, including Northern Ireland. But other than England, they have struggled to qualify for international tournaments, let alone progress — Scotland failed to make it out of the group stages of this year’s competition.

But Wales’ performances in recent years have not gone unnoticed among followers of the world’s most popular sport and Johnson, more of a rugby than football fan, is unlikely to forget them again.

The team faces Denmark in Amsterdam on Saturday in the first game of the tournament’s knockout stages after qualifying second in a group containing Italy, Switzerland and Turkey.

Before 2016, Wales had not reached a major tournament since the 1958 World Cup. It had produced some fine players in the intervening years, from Ian Rush of Liverpool to Ryan Giggs of Manchester United, but never a team.

But now a group has come together. And although Wales failed to qualify for the 2018 World Cup the country has risen from 116th to 17th in the world rankings over the past decade.

Gareth Bale of Real Madrid and Aaron Ramsey of Juventus are the stars, while several others are Premier League regulars. Yet half the squad of 26 play in England’s second tier championship and goalkeeper Danny Ward has not started a game for his club Leicester City in four years.

The team is a rare example of players who on the whole perform better for their country than their club sides. “They play for the badge and they play for the nation,” said Paul Corkrey, from supporters group Fans Embassy Wales.

Even the suspension of the team’s manager Giggs, who has said he would plead not guilty in court after being charged with assaulting two women, has not dented progress. Rob Page, his deputy, who coached many of the squad as youngsters, has taken over.

Laura McAllister, professor of politics at Cardiff University and a former Welsh women’s football international, said the Welsh FA had implemented a long-term strategy with the aim of improving the record of qualifying for tournaments.

National youth teams grow up together and a scouting system seeks out players born outside the country with Welsh ancestry. Striker Kieffer Moore, who equalised in the group game against Switzerland, was born in Torquay, England, but has a Welsh grandfather.

McAllister has argued football now beats rugby union in shaping national identity — a big claim in a rugby-mad country. The team also epitomises “an outward-looking, modern, diverse Wales”, she said, adding: “We think we can beat anyone on our day.”

In Wrexham, a heartland of football near the English border in north-west Wales, people agree.

“Wales is known for choirs, rugby and now soccer,” said Cyril Jones, 80, who was out with his wife Audrey buying a Wales football shirt for their adult son, who they will see for first time in 18 months when they sit down and watch the match together on Saturday. “I think soccer is getting bigger than rugby.”

Wayne Jones, a pub landlord who follows the team home and away, said it served Wales well to be treated like minnows of the game. “Wales like the fact they are considered massive underdogs,” adding: “They are a ‘band of brothers’ who like to upset the big boys.”

Jones’ pub, the Turf Hotel, inhabits a corner of Wrexham AFC’s Racecourse Ground and will host 107 people for the game. “Without social distancing we would get 300 in. We would have filled it easily,” he lamented.

Other businesses have been able to make the most of the football fever engulfing the nation. Chevron, a clothes shop in the town centre, has designed its own football-themed T-shirts.

Jamie Powis, the manager, tellingly said the one emblazoned with the entire team who beat Belgium — one of the world’s leading sides — in the quarter-finals of the 2016 Euros, had sold better than one featuring only Bale.

Shabab Anwar, whose family has run market stalls in Wrexham for more than 50 years, has sold out of big flags and bucket hats. “It’s been very busy. All the factories have ordered flags and bunting,” he said.

First minister Mark Drakeford, head of Wales’ devolved government, has also caught the bug. He posted a picture on Twitter watching one of the group games in his red, yellow and green bucket hat emblazoned with the “Spirit of ‘58”.

“We had a magical summer in 2016 following Wales all the way to the semi-final. Let’s hope that this year will be just as successful and exciting,” he told the Financial Times.

The Welsh FA has deliberately embraced Welsh culture, changing the name it uses from Wales to Cymru in 2016. But despite signs of rising support for independence — one poll shows 35 per cent in favour — McAllister does not think football can be harnessed by that cause.

“There is a political element to it. But you get that with any nation with a bigger neighbour. Sport is a way to distinguish yourself. Fans are not particularly bothered about independence. It is about uniting the nation,” she said.

Corkrey agreed and said few fans discussed politics. “I think it’s more cultural [than political], something to be proud of, like the rugby team.

He said it would have been great if more fans could have gone to the matches but coronavirus restrictions have made that difficult. The Netherlands has told Welsh fans they will not be allowed into the country under Covid rules, in contrast to Danish supporters. But Corkrey believes that plays into Cymru’s hands.

“Denmark have got virtually another home game in Holland, so Wales are right up against it as always, which suits us fine.”