• ‘The challenge is how do we get better as a team,’ says coach • England must beat All Blacks for first time since 2012

Eddie Jones has warned New Zealand that the best is still to come from his England side after they booked a World Cup semi-final showdown against the All Blacks.

England’s 40-16 victory over Australia was their biggest ever in a World Cup knockout match and they are in their first semi-final in 12 years. The Wallabies came back to 17-16 early in the second half but tries from Kyle Sinckler and Anthony Watson, to add to Jonny May’s first-half double, sealed one of the most impressive victories in Jones’s tenure.

But if they are to reach a third final they must defeat New Zealand at a World Cup for the first time after the All Blacks thrashed Ireland 46-14 .

England have faced New Zealand once under Jones, going down 16-15 last autumn, and have not beaten them since 2012. They met at the semi-final stage of the 1995 World Cup but, inspired by the 20-year-old Jonah Lomu, New Zealand romped to a 45-29 victory.

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“We just want to keep challenging ourselves,” said Jones. “We haven’t played our best yet and the challenge for us is how do we get better next week, how do we get better individually as a player, how do we get better as a team, and at these World Cups that’s what it’s all about.

“You go from a quarter-final to a semi-final, and the semi-finals are always probably the toughest game of the tournament because you’ve got two teams desperate to make the final. Everyone empties the tank, and you’ve got to find a way in the week’s preparation to get a little bit better. So our challenge this week as a playing squad and coaching squad is how do we find ways to get better.”

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Jones had earlier described the quarter-final as a “do-or-die” encounter. The Wales head coach, Warren Gatland, questioned how appropriate the comment was against the backdrop of the deadly typhoon that hit Japan. Jones, however, repeated the claim after the victory. “It was a do-or-die game,” he said. “Everyone understands that. The best samurais were always the guys who had a plan but who could adapt, who had a calm head and they were full of aggression. I thought we were pretty much like that.”

Jones was also full of praise for his captain, Owen Farrell, who he restored to fly-half after dropping George Ford to the bench in what came as a huge shock given how well the latter had played in the pool stages. Jones was pleased with how Farrell rallied his troops when Marika Koroibete scored his stunning try to bring the Wallabies back to within a point.

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“I was really impressed by the players in their ability to refocus and reset after we had a problem in the game, and that’s a great development of the team and a great job by Owen as captain.”

Farrell, meanwhile, praised his team’s response after Australia clawed the contest back. “The boys were calm and in control, and we had clear messages about what we were going to do next,” he said.

“The lads ripped into that and we managed to get some points back straightaway. This was a good performance, but we don’t feel we are at our best yet. We are probably going to have to be better next week, so we are looking forward to working that out.”

Koroibete was denied a second late try for a forward pass in the buildup but May pulled up when chasing back before going off and receiving attention to his left leg. He headed straight down the tunnel after the match but Jones said: “He just got a little bit of a twinge at the end of the game so we thought we’d take him off, but he should be fine.”

Australia’s head coach, Michael Cheika, bristled at questions over whether he would leave his role. Jones, however, insisted he had no sympathy for his compatriots. “It’s tough when you lose a game and particularly at this level of the World Cup,” he said. “At this moment, not a lot of sympathy no, because I’m enjoying the win and I think I’m allowed to enjoy the win. Maybe later in the week I might, so ask me that later in the week.”