England will head to France next weekend with the belief that an unlikely Six Nations title is “within arm’s reach”, with Steve Borthwick urging his players to improve on their remarkable victory against Ireland.

Marcus Smith’s last-gasp drop goal on Saturday sealed the most signi­ficant win of Borthwick’s tenure and sparked the kind of wild celebrations at Twickenham that have been all too rare of late.

England scored three tries for the first time since dispatching Chile in the World Cup pool stages, played with an attacking verve that supporters crave and finished the match with eight players with fewer than 20 caps, giving rise to optimism of a bright future.

Chandler Cunningham-South, who has impressed throughout this Six Nations from the bench, has been ruled out of the match against France on Saturday with a calf injury but replaced by the highly rated 20-year-old Newcastle back-row Guy Pepper.

Ireland remain heavy favourites to defend their title next week but should they slip up against ­Scotland in Dublin the door is open for ­England to leapfrog them, even if they would almost certainly need a bonus-point victory in Lyon to do so.

England have not beaten les Bleus in France since clinching their last grand slam in 2016 and though ­Borthwick is predicting “a bigger, physical challenge”, confidence is flowing after they shook the disappointing defeat by Scotland from the system. “I want to keep backing the players,” he said.

“We’re going to get things wrong, and we’re going to have to learn super-fast. And we have to learn super-fast what we did well and what we can do better because in seven days we’re playing another Test match. It is important to get tangible results. That is important for the team and my job is to reinforce that, and challenge us to be better next week.”

Ultimately, England may rue their failure to collect any bonus points from their four matches which makes a first championship in four years a more difficult task. The fact that they go into the final weekend of the championship still in the hunt for the title for the first time since 2020 is a sign of progress, however.

“A win like that at Twickenham is special but next week we’ve got to back it up because we’ve got a shot to win the championship,” the hooker Theo Dan said. “I don’t know exactly what results need to go our way but we’re within arm’s reach of winning a Six Nations and we’re in a really good place.” Asked if England believe they can win the title, he said: “100%. We’ve given ourselves a chance to do it.”

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Borthwick had noted how he felt the England jersey had weighed heavy on his players in the defeat by Scotland but praised their ability to brush off mistakes against Ireland. “I think the team went through a difficult experience at Murrayfield, reviewed it properly and then addressed it on the training field. The players weren’t perfect, they made mistakes, but at Murrayfield I thought we made a mistake and then went into ourselves, played a little bit small. [Against Ireland] they didn’t.”

Borthwick also reserved special praise for Ben Earl, who was named player of the match for the second time this championship. “I think he feels backed,” Borthwick said.

“I get the impression he feels he is growing as a player and he wants to keep getting better. I sat with him [on the morning of the game]. He talked and showed me what he wanted to do. And he pretty much did exactly what he said to me this morning. That is down to Ben Earl delivering that. It is phenomenal the thought process he is going through and how ambitious he is as a player to get better.”