England fans have been crying out for Southgate to release the handbrake and for his side to express themselves by putting an opponent to the sword.
After the controlled caution of the group stage and Tuesday’s historic win over Germany, England showed they can go up a gear or two by dismantling Andriy Shevchenko’s side with a blitz at the start of the second half.
It was a display to strike fear into Denmark, who await back at Wembley in Wednesday’s semi-final, as well as Italy and Spain, who will contest Tuesday’s other last-four.
After this showing, England will be clear favourites for the Euros – and why not?
It was not just that Southgate’s side played well. They also dealt with the very different conditions and the weight of expectation on their shoulders following the win over Germany.
But England showed neither, nor did they display the slightest nerves as Harry Kane fired them ahead inside just four minutes.
It was an early goal that dealt a hammer blow to Ukraine’s game-plan of containment and Shevchenko used an injury to rip up his back five mid-way through the first half and open up.
They did cause England problems before the interval, with Kyle Walker twice sloppy down the right but then England simply went up a level.
It was a welcome return to one of England’s strengths at the World Cup and they also would score their fourth from a set-piece when Jordan Henderson headed home Mason Mount’s corner for his first England goal.
In between, Kane scored again, nodding home Shaw’s cross.
That Henderson broke his duck and Shaw put on such a fine display in the new stomping ground of his biggest critic, Jose Mourinho, were just two of many enjoyable touches.
England also kept another clean sheet, surpassing their run of four at the start of the 1966 World Cup. They did not look impenetrable but they are so hard to score against.
At 4-0, Southgate could finally afford to look ahead, hauling off Kane, Sterling, Shaw, Declan Rice and Kalvin Phillips to save them for Wednesday and giving minutes to the likes of Dominic Calvert-Lewin.
England were expected to beat Ukraine and the Danes will present a far sterner test.
But still, it was difficult to imagine a more perfect and satisfying preparation for another European Championship semi-final at Wembley.
Kane answers critics… again
The England captain was dogged by questions during the group stage but no one is questioning him now, after another two goals to help England into the semi-final.
Kane needed just four minutes to follow his late clincher against Germany with another goal, stabbing home from Raheem Sterling defence-splitting pass, and he also scored England’s third with a header from Shaw’s cross.
You could see the confidence flowing back into Kane and he nearly clinched a hat-trick with a stunning left-foot volley which forced a fingertip save from Georgiy Bushchan. It did not matter for England, as Henderson’s goal came from the resulting corner.
In the World Cup three years ago, Kane went home with the Golden Boot but he peaked early – too early – by scoring all six of his goals before the quarter-final and drawing blanks against Sweden and in the semi-final defeat Croatia, when England needed him most.
Now, Kane is coming alive at just the right time and you would not bet against him finishing top scorer again, the way England are playing. If he is going to shine for only half a tournament, this is the way to do it.
By answering his criticism emphatically, Kane has done what he has always done. His career has literally been built on responding to negativity and proving people wrong.
He has done it again in the knockouts and Kane hopes that this time his efforts will end with the reward he has craved for so long.
Sancho and Shaw shine
Everything Southgate has touched during the tournament has turned to gold and the England manager got another big call right with the inclusion of Jadon Sancho.
The soon-to-be Manchester United winger is a proven talent and would’ve been in many people’s starting XI before the tournament but it was nonetheless another brave decision to start him.
Sancho had been in action for just 98 minutes since May 16 and his only previous appearance at the Euros was a six-minute cameo against the Czech Republic.
His inclusion meant Southgate resisted populism again by keeping fan-favourite Jack Grealish on the bench and continued to pick his side based on the opposition, rather than public sentiment.
In the Roman heat, with temperatures still up at 27C at kick-off, fresh legs felt important and Sancho had a terrific game. Occasionally switching flanks with Sterling, he terrorised his full-back in an eye-catching display of skill and direct running.
It was a reminder of England 18 months ago, when you wondered if Sancho-Sterling-Kane was the best front three in international football and Southgate always played with two pacy wingers.
It creates a welcome head to head between Sancho and Bukayo Saka to start against Denmark, assuming the latter is fit.
Throwing Sancho into England’s biggest game yet was also potentially a canny piece of man-management from Southgate.
It reinforced the idea that England need their entire squad and that no one is beyond contention – a powerful piece of messaging to his fringe players ahead of one of the biggest games in England’s history.
While on the left, Sancho also linked up superbly with his new club-mate Shaw, who is emerging as a player of the tournament contender.
Having been involved in both goals against Germany, Shaw added two more assists. His international comeback is one of the many stirring stories about these Euros for England.