In a World Cup that has teased and confounded expectations, England march mercilessly on. A familiar blend of the Stakhanovite and the sublime saw off Senegal, the champions of Africa. Now France, the reigning world champions, await in the quarter-finals next Saturday – along with the world’s most thrilling player, Kylian Mbappé.

England will be underdogs there, for sure. But the ruthlessness and efficiency of this 3-0 victory against Senegal, and the way they emerged from a sticky start to dominate, has laid down a significant marker.

Along the way, England also punctured the “curse” of playing on ITV. Since 1998, they had won just three of 16 World Cup games on the channel, a miserly 19% – compared with a win ratio of 71% on the BBC. Yet there were no ghosts here – only joy, and galloping expectations.

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Photograph: Caspar Benson

The only downside from the night came with the news that Raheem Sterling would be flying home after it was reported that armed intruders broke into his home.

“At the moment, clearly the priority is for him to be with his family,” the England manager, Gareth Southgate, said. “We’re going to support that, and leave him to have as much time as he needs. He’s going home. Sometimes football isn’t the most important thing, and family should come first.”

This was a game that neatly split into thirds: the first tense, the second explosive, the last a nonevent as by then England were three goals to the good thanks to Jordan Henderson, the captain Harry Kane and Bukayo Saka.

No wonder Southgate was delighted afterwards, praising not only how hard his team had worked with and without the ball, but what he called “the ruthlessness of our execution”.

“We were a bit sticky with the ball in the first 25 to 30 minutes,” he said. “But the team have made a very complicated game look straightforward. We’ve got some super young players, and it’s been right to give them their head and their opportunity. These games are a brilliant life experience for them. Their progress is phenomenal.”

Now, though, the difficulty ratchets up several levels – starting with France on Saturday. The world champions took time to ease through the gears before brushing past Poland 3-1 earlier on Sunday, but it was the sight of the extraordinary Mbappé hitting top form that will most worry Southgate’s side.

The 23-year-old was an omnipresent menace with his pace and trickery and also scored twice, lashing his first past Poland’s keeper Wojciech Szczesny despite the shortest of backlifts before foot struck the ball, and then arced an even better second into the top corner.

That strike was celebrated with a calm victory salute to his supporters, not unlike a commander in chief acknowledging his rank and file after battle. He now has the most World Cup goals scored by a men’s player before turning 24, ahead of Pelé. That is the rarefied atmosphere he now inhabits.

Southgate also recognises the challenge that now awaits. “France are an outstanding team with a phenomenal tournament record and some outstanding individuals,” he admitted. “So without a doubt it’s a game where we’ll have to find our highest possible level.”

True enough, but there are reasons for cautious optimism, England having galloped into the last eight without losing a game. Only the Netherlands among the other favourites have such a résumé. They have also scored 12 goals and conceded just three. That is best in class too.

At the same time, Southgate knows that England are yet to face a major test. Their group opponents Iran and Wales were among the weaker teams in Qatar – while Senegal were without their talisman, Sadio Mané, and their midfield terrier, Idrissa Gueye. England’s defence, as they showed in the first half, retains its capacity to induce palpitations even in the calmest moments.

However England have an emerging star of their own in 19-year-old Jude Bellingham, who put in another display suffused with maturity and class.

“I don’t want to big up Jude too much because he’s still young, but he’s one of the most gifted players I’ve ever seen,” histeammate Phil Foden insisted. “I don’t see a weakness in his game. He’s got everything, and he’s going to be the best midfielder in the world, for sure.”

England fans are yet to arrive in Qatar in weighty numbers, but that will surely change as this World Cup heads into the latter stages. It meant that the largest noise in Al Bayt Stadium was often generated by a small pocket of Senegalese fans, who swayed and clapped in time to a relentless barrage of drums. One even wore a giant lion’s head, in honour of Senegal’s nickname, the Lions of Teranga.

Their team played like lions too early on, at least in the early stages, and had the better chances – with Pape Sarr shooting over from six yards and Jordan Pickford being forced to save smartly from Boulaye Dia.

But once Henderson put England ahead after 38 minutes, they grew in confidence and stature. Senegal’s manager Aliou Cissé urged his team to stay calm. But they were clearly rattled. Moments later Kane scuffed a chance over the bar, before smashing home a second just before half-time. Soon after the break Saka added a third and it was game over.

Kane, who scored his first goal at this World Cup, now sits just one goal behind Wayne Rooney on the England all-time scorers’ list. But his thoughts are focused elsewhere. “We’ll enjoy this one, but our focus turns to France,” he said. “It’ll be a really tough game, they’re reigning champions, it’ll be a good battle. We’ll recover nicely and get ready for the game.”

Bellingham, meanwhile, heaped praise on fellow midfielder Henderson, who has been a surprise starter in Qatar. “I see some of the rubbish that was said about him playing. Honestly, it’s ridiculous. He’s delivered again in a big game, so I think it’s time he gets a bit of respect.”

The same could be said about England. France, however, will be a supreme test of their credentials.