Christian Eriksen's spot kick, moments after Harry Maguire's dismissal, gave the visitors victory.
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Denmark boosted their chances of reaching the finals thanks to Christian Eriksen's winner from the penalty spot against an England team who had two men sent off at Wembley Stadium.England vs Denmark: as it happened, reaction
Match in brief
England dominated much of the first half but the contest turned in the 32nd minute when Harry Maguire was dismissed for his second bookable offence. The visitors quickly exploited the situation as Thomas Delaney was fouled by Kyle Walker in the area and Eriksen dispatched the penalty past Jordan Pickford.
The home side regrouped at the break and Mason Mount nearly levelled only for Kasper Schmeichel to keep out his header from point-blank range. Daniel Wass headed over Pione Sisto's cross as Denmark threatened a second, but they had done enough to leapfrog their hosts into second place in Group A2 behind Belgium.
Simon Hart, England reporter
A first home loss in two years brings England back to earth with a bump three days after the win over Belgium. There was much to be positive about in a bright opening half-hour, not least the efforts of Mason Mount and Reece James, but Maguire’s red card, continuing his unhappy start to the season, proved a turning point. England showed resilience yet the red card for James after the final whistle left another question mark against their discipline and soured an otherwise impressive full debut.
Sture Sando, Denmark reporter
The match wasn't pretty but it's a massive result for Denmark – winning at Wembley for the first time since 1983, and keeping one of the best teams in the world from scoring over two games. Denmark will remain in League A for another campaign with November's matches against Iceland and Belgium now for a place at the finals and not potential relegation.
Christian Eriksen, Denmark midfielder: "It feels special. First and foremost to have played 100 matches [for Denmark], but also to beat England at Wembley. I knew before the match that we hadn't done that in 37 years. So it's extraordinary to stand here as a winner."
Simon Kjær, Denmark captain: "I'm proud to be captain of this team and to have reached 100 matches. This is a giant milestone that not many Danish players have reached. I'm not done yet. I still have many matches in me, and there's a lot we can and will achieve. We want to beat the big boys, and that started today. We are a team with quality, we believe in ourselves. This is a step in the direction we want to go."
Declan Rice, England midfielder: "Until the sending-off I thought we were playing really well and using the ball really well. Reece James and Mason Mount were creating some great chances for us but we just couldn't put the ball in the back of the net. We knew if we carried on playing like that then a goal was coming, but then the red card and automatically the game swings into their favour."
Harry Kane, England striker: "I'm proud of the boys, they gave it everything. We had control until the red card, we conceded the penalty straight after. We dug deep, they didn't create many chances and we created some and on another day they may have gone in. In big games mistakes can cost you and that's what happened. It's great preparation going into the EUROs next year, it's a good experience for going forward."
• England had won 20 of their last 21 competitive home games before this defeat.
• Denmark have lost just twice in their last 40 games.
• Denmark have kept a clean sheet in six of their eight UEFA Nations League matches.
• Christian Eriksen has scored 24 times in his last 35 internationals.
• Simon Kjær and Christian Eriksen both won their 100th cap for Denmark.
England: Pickford; Walker, Coady, Maguire; James, Mount (Sancho 73), Rice (Henderson 76), Phillips, Maitland-Niles (Mings 36); Kane, Rashford (Calvert-Lewin 72)
Denmark: Schmeichel; Wass, Kjær, A Christensen (M Jørgensen 46), Skov (Mæhle 46); Delaney, Eriksen, Højbjerg (Jensen 88); Braithwaite (Vestergaard 73), Dolberg (Sisto 37), Y Poulsen