England head coach Eddie Jones says his side have not hit their best yet after they powered past Australia to reach a first World Cup semi-final in 12 years.

After a strong start from the Wallabies, England stormed to a convincing 40-16 win with a performance that prompted Jones to compare his players to samurai.

"The best samurai had a plan they could adapt," he said. "They had a calm head but were full of aggression.

"We were pretty much like that today."

Jones added: "But the challenge is how do we get better because there's always a better samurai around the corner. We haven't played at our best yet."

The "better samurai around the corner" could be three-time champions New Zealand, who will be England's semi-final opponents after the All Blacks' 46-14 victory against Ireland later on Saturday.

England looked threatened when faced with a fast start by the Wallabies, but soon recovered to lead 17-9 at half-time thanks to two tries from Jonny May.

Their advantage was cut down to one after a brilliant solo score from Marika Koroibete, but tries from Kyle Sinckler and Anthony Watson and 20 points from the boot of Owen Farrell sealed the win.

The only worrying sight for England fans was May pulling up just before full-time, seemingly because of pain in his leg, but Jones said it was a "twinge" and that the wing "should be fine".

'We're making sure Billy's wife stays'

England coped well with their greatest test of the World Cup so far after cruising through the pool stages, recording their biggest winning margin in a World Cup knockout game.

There were stand-out performances in England's forward pack, with Jones particularly praising the back row.

Tom Curry was named man of the match after teaming up with Sam Underhill to take on veteran Wallabies Michael Hooper and David Pocock.

But Jones saved his highest plaudits for number eight Billy Vunipola, who played 80 minutes after not taking part in full training last week because of an ankle injury sustained against Argentina.

"The effort from Billy, given he's only done a couple of training sessions, was outstanding," Jones said.

"Maybe it's helped him having his wife here, so we're going to make sure his wife stays next week."

'George Ford was spectacular'

The absence of George Ford in the starting XV was the major talking point after the team announcement on Thursday, with the fly-half named among the replacements for the quarter-final.

Instead, captain Owen Farrell started at 10, with Henry Slade and Manu Tuilagi the centres.

The choice to include Slade, who had not played more than a half of rugby in five months because of a knee injury, seemed to be justified when the Exeter back placed a kick perfectly to set up May's second try.

Ford came off the bench in the 61st minute and the Australian said his performance was "spectacular".

"We were pleased with the selection," Jones added. "Slade did a great job and Ford came on and filled his job superbly.

"I did not drop Ford, I changed his role and it was brilliant. Are we vindicated? We're happy that he played his role well. Modern rugby is a 23-man game.

"Whether he plays 10 next week, we're not sure."

Analysis - a phenomenal England machine

Former England scrum-half Matt Dawson on Radio 5 Live: "We saw a phenomenal England machine. But I cannot believe anyone would do that and hand it to you like today. It was rugby suicide from Australia.

"England can improve, be more accurate. They gave six penalties away in the first half. There is room for improvement, but what England will get is that it was a genuine test, that brought them into this tournament. They won't train a lot this week, mentally they will be right for next weekend."

'We've gone up a gear - what the players said'

England captain Owen Farrell: "I thought Australia made that a brilliant game. They attacked throughout but our boys did well in defence and managed to get some field position off the back of it. We know when we have field position we can be pretty dangerous.

"We did what was needed. We had the lead and Australia were throwing everything at us again. We wanted to play the game at our pace and we did that in the second half.

England scrum-half Ben Youngs: "Australia play the way they play, you know they will chuck it about and they caused us problems.

We stuck in there, the key point was midway in the second half on our line when we pushed them back, pushed them back. We were probably cruising in second gear in those first few games, but we went through the gears today."

England centre Henry Slade: "There were a couple of sticky periods either side of the half-time but the heart the boys showed then was massive. The way we dug our heels in and then moved on is a great sign for the boys.

"It was a really good performance and result, we can rest up now, watch the other three games and prepare for the semi-finals."

Social media reaction - 'Very impressive England'

Former England centre Mike Tindall: Well played England, been asking for a performance that leaves the fans going 'we can win this!' Think that was pretty close!

Former England hooker Brian Moore: Very good performance by England. Most impressive aspects of the win were the decision-making and game management - mostly spot on.