The Three Lions took an early lead, in the first-half but were pegged back by the well-organised Danes shortly after with no further goals after the break.
England remain in a good position to qualify for the next phase of Euro 2024, with the final Group C game against Slovenia to come next Tuesday.
There was a scare for England after just nine minutes when Kyle Walker sat down on the grass after going over on his ankle awkwardly on a surface that was cutting up alarmingly in the opening stages.
TV replays showed a painful-looking twist as he crossed the ball in, but thankfully, after a change of boots, he was fine to continue.
On the 13 minutes, Phil Foden was left cursing himself after finding a pocket of space on the edge of the box, jinking past one challenge before curling a shot over the bar from 15 yards.
Five minutes later, England took the lead.
Danish left-back Victor Kristiansen was in two minds as he sized up a back pass to his keeper, allowing the jet-heeled Walker to pinch the ball off his toes, drive into the box and his twice-deflected cross fell kindly to captain Harry Kane who calmly slotted past Kasper Schmeichel with 18 played.
England had the momentum but failed to take the game to Denmark and instead, the Danes grew in confidence and on 33, equalised.
A poor Kane clearance gave possession to Denmark and with no challenge or press, Morten Hjulmand was able to drill a low 30-yard shot in off the foot of the post to make it 1-1.
England were sloppy with the ball and lacking in energy and spark, with several of the players looking frustrated as they went in at the break.
There was more of the same after the re-start, with too many misplaced passes and a lack of cohesiveness from the Three Lions.
However, on 55 minutes, Foden - continually serenaded by England fans throughout - came close to restoring the lead when he sent a 20-yard drive against the post with Schmeichel well beaten.
John Stones was his usual composed self when called upon, but had few chances to surge forward and affect the game in the Danish half.
Foden‘s evening was ended on 68 minutes when he was replaced by Eberechi Eze.
Little of note happened in the time that remained, with the Danes far happier with the point than the legions of England supporters.
Kyle Walker said after the game: “We take away the point and we are top of the group - I cannot stand here saying it was a fantastic performance.
“Collectively we need to know when to go or when not to go. We have to go as a full team and that is something we need to practice because you come to the knockout stages and slight things like that can cost you.
“Our build-up play can be better. And making sure the second ball is our ball.
“Each individual player is representing their country so they are going to give their blood, sweat and tears and we are doing the exact same..
“There’s no complaints about anything - we have everything we need here - it’s all about the 11 players on the pitch.”
Meanwhile Spain booked their place in the Round of 16 with a 1-0 win over Italy.
Rodrigo played the full 90 minutes in a game dominated by La Roja,
Riccardo Calafiori’s unfortunate own goal on 55 minutes settled an entertaining game, with Rodrigo giving his usual polished performance.
The City anchor almost scored on 29 minutes with a sweeping low drive from the edge of the box that was looked goal-bound before it was blocked by an Italian defender.
Our No.16 picked up a yellow card for protesting after team-mate Marc Cucurella was fouled and the perpetrator went unpunished.
Spain wrap up their group stage phase against Albania next Monday.
