Gareth Southgate has called Harry Kane “irreplaceable” and praised the striker’s mental strength, selfless work ethic and ruthless finishing after the captain scored England’s first World Cup hat-trick for 32 years to help propel the team into the knockout phase.

Kane moved clear of Cristiano Ronaldo and Romelu Lukaku in the race for the Golden Boot by taking his tournament tally to five in a 6-1 thrashing of Panama, England’s biggest win at the finals, despite having played only 153 minutes. Only Gary Lineker has scored more times for the national side at the finals. Kane departed clutching the match ball and with his team safely through to the last 16 with Thursday’s final group game against Belgium to come.

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The 24-year-old has made no secret of his desire to establish his reputation alongside players such as Ronaldo and Lionel Messi at this tournament. “Clearly the stage to do that is this one,” said Southgate. “He’s started brilliantly. The penalty … you can dismiss penalties as easy, but the length of time he had to wait and the number of distractions which made him refocus and start again; that tells you about the mental toughness he has got.

“He’s there in the scoring charts. He’s up at the top. We wouldn’t swap him for anyone in the tournament in terms of No 9s because you know that, when he gets opportunities, he’ll bury them. Just as important is the way he presses, holds the ball up, contributes to the overall game, and sacrifices himself for the team.”

Southgate intends to freshen up his side on Thursday, when leadership of Group G will be determined, but will seek to maintain “squad harmony” when it comes to selection for the game in Kaliningrad. The manager spent the entirety of England’s 2002 World Cup campaign unused by Sven-Göran Eriksson and, despite too many changes potentially disrupting rhythm, is reluctant to put his fringe players through similar frustration.

“Over the next 36 hours or so we have to decide what our priority is and, for me, the harmony of the group is very high on that list,” said Southgate, who allayed fears over Kieran Trippier’s fitness and hopes to have Dele Alli available against Belgium. “Before the tournament we had a good performance against Costa Rica with a different XI to those who played against Nigeria a few days earlier. I have complete trust in all the players. We’d look a bit different because of the profile of players in certain positions but I know we’ll get a high level of performance. At this moment my thoughts are with the players who haven’t played as much, but I have to consider everything before I decide upon my team.

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“The harmony of the group is important to me. The three players we brought on today are really critical in terms of what we do in training and for their enthusiasm around the group. There are others who we didn’t get into the game. Some have been a couple of weeks without a match and we’re going to need more people ready as we get further into the tournament. But we want to keep playing well and keep the consistency in our play, too; to keep the momentum going and keep progressing as a team.

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“We have to make the players who haven’t played matches feel valued. Their approach to training, their intensity, meant we were ready for this game. If that was to dip, we’d be nowhere near as effective.

“I’m pleased for the squad and the staff today. I’ve heard talk of it being better finishing second but how do you work all that out, really? Let’s go and enjoy it again. It’s nice, it’s a game where we’re not up to our neck in pressure, but we also want to keep winning football matches. It’s a nice decision to have.”