The Three Lions' only previous triumph on the world stage came on home soil 52 years ago, culminating in a 4-2 win against West Germany in the final at Wembley Stadium.
Southgate's current crop are just two wins away from writing their own names in English folklore, though, with Croatia up next in the semis and then potentially one of France or Belgium in the final.
Ahead of Wednesday's showdown with Croatia at the Luzhniki Stadium, Southgate has called on his players to make their own history.
"We've talked, touched briefly, certainly, on the team which won," he told reporters. "How they're still held and revered. [It was] at the beginning of working together with the lads and trying to sell them the vision of what's possible, what we're looking to achieve in the long-term.
"We have had events on in camp when some of those guys have been in, when the road was named at St George's Park after Sir Alf [Ramsey].
"I've met quite a few of those players and we know exactly how they're held and perhaps, in the modern era, that would be even crazier. Social media and everything else, the global thing is so much bigger."
England's quarter-final win against Sweden on Saturday afternoon was watched by a TV audience in Britain of almost 20 million.