"Wednesday's cancelled! Fans go wild as Three Lions reach first World Cup semi-final for 28 years," said the Sun on Sunday after England beat Sweden 2-0 in the Russian city of Samara.
The Mail On Sunday online edition said: "The Dream Goes On! England in ecstasy."
It praised the emerging star of the England team, goalkeeper Jordan Pickford, for more "heroic saves", and said 32 million people had watched on TV.
The Sunday Mirror paraphrased the song written when England hosted the 1996 European Championships, saying: "England are in the World Cup semi-finals – could this really be the summer football comes home?"
The broadsheet Observer said in its report: "At the final whistle, the victorious players converged on one another. It took a few seconds for them to gather their breath and then, finally, they could join the party that was already under way behind the goal to their right."
Despite the euphoria, the paper found fault with England's victory.
"If we were to be picky, a legitimate argument could be made that England will need to play with more finesse if they are to harbour serious ambitions of winning this competition."
The Sunday Telegraph said Southgate "has liberated England and now the country's ambitions ought to be higher than 1990" when they last appeared in a semi-final, losing to West Germany.
The paper compared Southgate to the England coach 28 years ago, Bobby Robson.
"The similarities between Southgate and the late Sir Bobby are striking. Both are synonymous with modesty, consideration and togetherness.
"Like Robson, Southgate has struck gold by playing three at the back and encouraging freedom of expression while backing youth."
- Maguire, Alli score for England -
England's progress earlier in the day was much more serene.
Leicester defender Maguire headed in the opener from a corner on 30 minutes -- England's eighth goal from a set-piece at the World Cup -- with Alli adding a second, also from a header, just before the hour.
Man-of-the-match Pickford made three outstanding saves to keep Sweden at bay, further burnishing a reputation that has grown throughout the tournament.
"It's a great achievement for the team, we owed it to the fans back home who believed in us," said Alli.
"It's always nice to score, especially on occasions like this. It's an amazing feeling to be going to a semi-final at a World Cup."
The tournament's leading goalscorer Harry Kane failed to find the net for the first time in the competition, but the England captain said confidence was high after posting the country's best run at a major tournament since Euro '96.
"We're buzzing. We know there is still a big game ahead, but we're feeling really good," he said.
As England basks in a long heatwave, life came to a standstill for the match, with fans watching the game on big screens at events up and down the country.
The party began with beer showers and chants of "Football's Coming Home" -- England's unofficial football anthem written for the Euro '96 tournament.
Prince William, the president of the Football Association, praised Southgate's men.
"You wanted to make history @England and you are doing just that," he tweeted. "This has been an incredible #WorldCup run and we've enjoyed every minute. You deserve this moment – Football's Coming Home!"
Even if Southgate's team reach the final, William will not attend the match because of Britain's diplomatic boycott of the World Cup in Russia over a nerve agent attack in England this year.