The Danes have been getting steadily better after a poor start but England have been consistent throughout and their success has been built around a tight defence, which has not conceded a single goal yet.
Raheem Sterling and Harry Kane have scored three goals each and have been linking up well in attack.
The last time England played Denmark in a major tournament - in Niigata, Japan during the 2002 World Cup - they ran out winners 3-0 but lost to Brazil in the next match.
Today is the day.— Boris Johnson (@BorisJohnson) July 7, 2021
Come on England! 🏴 pic.twitter.com/x4lhG92mrp
But England's main problem could be a mental block - the team have not reached the final of a major tournament since they won the World Cup in 1966.
Here is a reminder of some of those painful matches.
England 2 West Germany 3 - 1970
England were the holders going into the 1970 World Cup in Mexico but their preparation was impaired when captain Bobby Moore was arrested for stealing a necklace in Colombia, where the team had been undergoing altitude training.
Alan Mullery and Martin Peters had put England into a 2-0 lead and it looked like nothing could stop them.
But the Germans were determined to avenge their 1966 defeat and came back with goals from Franz Beckenbauer and Uwe Seeler in the second half.
The game went into extra time in the searing Mexican heat and in the 108th minute Gerd Muller broke English hearts.
Argentina 2 England 1 - 1986
After Sir Alf Ramsey retired as manager, England struggled at the international level, failing to qualify for the 1974 and 1978 World Cups, getting knocked out early in 1982 and doing little at the European Championships.
But Bobby Robson took over as England manager in 1982 and four years later hopes were high, as a team which included strikers Gary Lineker and Peter Beardsley, midfield star Glenn Hoddle, and legendary goalkeeper Peter Shilton headed off for another World Cup.
Mexico hosted the World Cup again that year after Colombia pulled out for financial reasons.
Lineker's goals pushed England through to the quarterfinals and, in front of 114,000 people at the Stadio Azteca in Mexico City, they faced Diego Maradona's Argentina.
Four years earlier, hundreds of Argentinian soldiers and sailors perished during the Falklands War and the men from Buenos Aires were determined to gain revenge on the football pitch.
In the 51st minute Steve Hodge's fluffed clearance looped up in the air and Maradona challenged Shilton for the ball.
Seconds later the ball was in the net and despite furious protests, the referee refused to disallow Maradona's notorious "Hand of God" goal.
Four minutes later, Maradona danced around half the England team to score a sensational second goal and despite Lineker's late goal it was time for the English to head home.
England 1 West Germany 1 (lost on penalties) - 1990
In 1990, England's team relied on Lineker's goals again but also the magisterial talent of midfielder Paul Gascoigne.
England overcame Belgium and Cameroon but needed extra time in both matches and were into the semifinals, where they would play their old adversaries West Germany for the right to play Argentina in the final.
Andy Brehme put West Germany ahead but Lineker equalised on the hour and then, in extra time, Gascoigne was booked for a foul.
The booking meant he would miss the final and he was on the verge of tears. It would become an iconic moment in English football history.
The game went to a penalty shootout and the Germans scored four in a row while England left back Stuart Pearce - nicknamed "Psycho" - missed and when Chris Waddle put his over the bar they were out.
England 1 Germany 1 (lost on penalties) - 1996
In 1996, England hosted the European championships and comedians David Baddiel and Frank Skinner composed a catchy song - Three Lions (Football's Coming Home) - which captured the "30 years of hurt" and the endless optimism of England fans.
England played well in the tournament - famously dispatching the Dutch 4-1 with a bravura performance - and again reached the semifinals.
The opponent would be...Germany, of course.
Alan Shearer headed England into an early lead but Stefan Kuntz equalised in the 16th minute.
The game went into extra-time and England came agonisingly close to scoring the winner - Darren Anderton hit the post and Gascoigne was a whisker away from converting a cross by Shearer.
But it came down to penalties.
Germany were again flawless - scoring six in a row - and England also dispatched five without error.
Up stepped defender Gareth Southgate and his penalty was saved.
Southgate today is the England manager and he mentioned the penalty miss in the run-up to last week's victory over Germany.
England 2 Portugal 2 (lost on penalties) - 2004
Portugal were hosts of the European championships in 2004 and in the quarterfinal in Lisbon they faced England.
Michael Owen gave England an early lead but with just seven minutes to go Helder Postiga equalised.
In the 90th minute Sol Campbell's goal was disallowed for reasons only the Swiss referee could explain.
Portugal took the lead in extra-time but Frank Lampard equalised with only five minutes left on the clock.
The game went to penalties again and Portugal won it after David Beckham and Darius Vassell missed their kicks.
England 1 Croatia 2 - 2018
In the 2018 World Cup in Russia, England played well under manager Gareth Southgate and made it to the semifinal where only Croatia stood in the way of them reaching their first major final in 52 years.
Once again England struck early with a sensational Kieran Trippier free kick after just five minutes.
But Ivan Perišić equalised in the 68th minute and as the game went into extra-time England tired and Croatia came on strong.
This time England fans were praying for a penalty shootout but it was not to be, with Mario Mandžukić scoring the winner in the 109th minute.
Croatia were defeated 4-2 by France in the final while England fans were once again left with a feeling that their team had choked again.