Against Panama, a nation whose name is more associated with hats, England could do with scoring a hatful – especially if those goals are shared around. And especially if not all of them are scored by a certain Harry Kane.

The history of English football would more than suggest it is foolish to count on any positive result involving the Three Lions but, privately at least, Gareth Southgate will hope that when they come off the pitch on Sunday afternoon in the searing heat of Nizhny Novgorod after facing Panama in their World Cup Group G encounter, it will not again just be about his captain.

“We wish we had Kane!” was the headline in the German newspaper Bild earlier this week following the striker’s two-goal, match-winning contribution to England’s precious victory over Tunisia and if a publication from the homeland of the world champions is saying that then Southgate knows he has a special player and a special talent in Kane. But the England manager knew that anyway, which is partly why he gave Kane the armband, and partly why also Kane did not do the pre-match media duties here which were taken on by Southgate’s “second captain”, Jordan Henderson.

Otherwise there would have been more questions about Kane’s desire to win the Golden Boot as the World Cup’s leading scorer, especially after another brace from Belgium’s Romelu Lukaku, and a reinforcement of the theory that this is the Harry Kane team.

Of course, all that matters is the win and if that comes courtesy of one, two or three goals by Kane then who cares? If England win they are in the last 16, which will also be only the second time in their last 15 major tournaments that they have won their opening two games. Whatever the opposition that is not to be sniffed at.

Their final Group G fixture is against Belgium, who may well be resting Lukaku and Eden Hazard, and the numbers those two have produced in recent games have been seriously impressive. Lukaku has scored 23 goals in his past 20 games for Belgium, with four assists. Eden Hazard has 11 goals and 11 assists. For England only Kane can challenge that. So who is going to be England’s Hazard to Kane being their Lukaku? It is an issue that Southgate is across. If England are going to be serious challengers then someone else has to step up and he was asked about it – not for the first time – at his press conference. “We’re trying to get a forward line that is exciting in its movement and has scored goals at club level,” Southgate said.

“In the end, that will come if they keep getting in the right areas and making the right runs, creating the chances we did the other night [against Tunisia]. The goals will come. We have an outstanding goalscorer as a No 9, and people like [Jamie] Vardy with an exceptional record in big matches as well. Danny Welbeck has a lot of goals [16 for England, one more than Kane]. You want goals coming from all areas.

“Frankly, though, it doesn’t matter who scores in a tournament. If Harry hadn’t scored, we’d have been answering questions about him.”

Which is true. But the statistics are a serious concern. Kane, Dele Alli – who is out injured – Jesse Lingard and Raheem Sterling have 91 goals between them in club football last season but only one is scoring for his country. In fact it is just five goals in 73 England games for Sterling, Alli and Lingard combined and the stats do not get any better however you analyse them.

Sterling has not scored for England for 987 days and has just two goals in 38 appearances – the equivalent of a full Premier League season – and those goals were against Lithuania and Estonia. Alli’s last goal came in Oct 2016, when he scored against Malta, and he has two goals in 26 appearances while Lingard has one goal – his recent strike in the friendly against Holland – from 13 caps. Marcus Rashford, who may well replace Sterling, has scored just three times in 20 games.

No one can doubt England’s intent and they are certainly living up to Southgate’s edict to attack the tournament. But they could well have thrown away two points with their wastefulness against Tunisia and there is a serious lack of ruthlessness in front of goal – the kind of ruthlessness that contenders must have.

Southgate simply has to get more goals in the England team and more goals from someone else but Kane. It is no disrespect to Panama that facing them offers a good opportunity, even if the 55th-ranked nation in the world, at their first World Cup, and with a domestic league that is less than 40 years old, have a far stronger defensive record than might be expected and are not afraid to be physically rugged in maintaining it. They may have conceded three against Belgium and six in a recent friendly against Switzerland but in five other matches just two goals have gone against them.

Against that, England have only scored more than two goals twice in their past 28 matches and going into this match have a goal difference of five inferior to Belgium who thumped Tunisia 5-2. It means, unless England go goal crazy, that Belgium will need only a draw on Thursday to win the group. That is if they want to win the group – the route forward appears more comfortable for the runners-up, in fact, which may partly explain Roberto Martinez’s suggestion he would leave out big names (Dries Mertens is another).

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For England and for Southgate the permutations do not matter, not until Panama have been negotiated, and even then there is a theory that the manager will try and build on momentum and confidence by wanting to beat Belgium and therefore take a big scalp.

Part of that confidence building is what Southgate’s assistant Steve Holland called improving “the balance of goalscorers in the team”. That means someone else, and not just Kane who, in fairness, has only just claimed his first goals in a major tournament, although it is also 10 in 10 under Southgate, taking responsibility. “He’s the one player that has the track record at this level that you can bank on,” Holland said of Kane. But England need more than one player to hang their hat on.