Buoyed by their impressive performance and last minute victor against Tunisia on Monday the Three Lions produced a breathtaking first half display that saw John Stones score two headers, Harry Kane blast home a brace of penalties, and Jesse Lingard sore a stunning goal from outside of the area.
The Tottenham striker scored his third and England's sixth, deflecting a Ruben Loftus-Cheek shot into the net, before he was taken off and replaced by Leicester striker Jamie Vardy.
Looking ahead to England's next opponents, Southgate said that he had a good idea of what to expect from a Belgium team tipped to go a long way at the World Cup. "You go out there to win a game - the other bits are nonsense".
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So if you had two incredibly cynical managers in charge of England and Belgium, both teams could play for a goalless draw and try to get their entire team, plus substitutes if required, booked, in an attempt to swerve the favourites.
A victor of 57 England caps as a player, Southgate has earned rave reviews for creating a more relaxed and open environment between players, press and fans.
"We are just enjoying it", said Kane.
Travel organisation ABTA said there has been a spike in "World Cup fever" among England fans who stayed home initially but are now booking last-minute trips.
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England's final group game comes on Thursday evening when they take on Belgium in Kaliningrad. "England is totally spectacular, a lovely team", said Panama coach Hernan Dario Gomez, who went into the English changing room at half-time to congratulate Southgate.
"I don't know how Gareth could send those lads out there and say, "We need to get a draw today" or "We need to get more yellow cards". They are architecturally lovely", Southgate said.
"I think there's a big performance coming from England and it's just bubbling".
Travel firm ABTA added: "It's been World Cup fever since England's win in the first game".
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National team captain at 24-years-old, the youngest player to wear the armband at this summer's tournament, Kane also became the first player to score a brace at a World Cup for England since Gary Lineker in 1990.
"We're a team who want to play and you see that on the pitch from the back to the front".