England moved into the World Cup semi-finals for the first time since 1990 with a 2-0 win over Sweden on Saturday.
They face Croatia on Wednesday for a place in the final where they will meet either France or Belgium.
And Hurst thinks they can go all the way, and says Southgate is the new era Ramsey.
“In terms of similarities, the leadership at the top is vital,” Hurst said.
“We had a terrific manager in Alf Ramsey, who had a great system and he selected a team that could be successful and had good characters.
“We’ve seen the leadership with Gareth Southgate being very impressive, which has engendered a good team spirit. That seems to be quite evident, with what he says, how the team are celebrating with each other – we’re not seeing any bad stories.
“The difference for me is we had four world-class players at the time, whereas I don’t think you could say that at the moment.
“If we get through this and do well at the next tournament, we’ll be talking about them as world class.”
One of the biggest calls Southgate made prior to departing for Russia was to elect Tottenham forward Harry Kane as his captain.
It has proved a shrewd move, with Kane not only providing a tournament-leading six goals so far but also impressing Hurst with his leadership qualities.
“He’s been terrific – scoring goals and playing wise,” Hurst added.
“As a guy selected to lead the group, it was a very good decision. Remaining grounded as a captain also helps to generate team spirit if your leader is popular.”
England failed to get out of the group at the previous World Cup and two years ago they were embarrassingly dumped out of Euro 2016 by Iceland.
Even after being drawn in a favourable group this time around, few thought they would still be active in the final week of the World Cup but Hurst believes they could be crowned champions following Saturday’s quarter-final success over Sweden.
“You wouldn’t have said we were going to win beforehand,” Hurst added.
“(But) where we are today, I would say, categorically, quite clearly, we can win it, without a shadow of doubt.
“Croatia look a very good team, (they have) very good players in (Luka) Modric and (Ivan) Rakitic, they look a dangerous side.
“I would say I would be disappointed if we didn’t beat them. If you’d have said we could be in the semi-finals, play Croatia, would you want that? We’d say, ‘Yes’.”
