Australia have a realistic chance of raising the Rugby World Cup for a third time if they continue to be as brutal and clinical as they were at Twickenham, where, in the most humiliating fashion, they put England Rugby into a tailspin.

Twickenham crowds don't often boo their team off the field or their national coach when he is being interviewed post-match. But such is the widespread despair in a country after an opposition they thought was their whipping boy inflicted the most embarrassing of blows.

A World Cup host nation is not supposed to be knocked out of contention well before the end of the pool stage, but the fact that Australia did it with such consummate ease just adds to the nation's pain.

England were supposed to once again expose Australia's allegedly dud scrum. Not so. They were instead the ones who disintegrated, being shoved around, split apart, suffering six scrum penalties. They even had to replace their props because Sekope Kepu and Scott Sio refused to be intimidated. The heart and soul of England Rugby was no more, hilariously shown up by an opposition they have mocked for so long for being set-piece marshmallows.

Bernard Foley of Australia goes over to score their second try against England© Paul Gilham/Getty Images

England were supposed to expose Wallabies No.10 Bernard Foley, and his tendency to lose his way in big matches. Not so. Foley was near untouchable, producing the performance of his life. He had a near faultless game, producing the tries, kicking the extra points, and showing the poise required from a playmaker to see a team grow and thrive in a World Cup tournament.

They thought they could counter Australia's 'Pooper' back-row combination. Instead, David Pocock and Michael Hooper reigned supreme, especially at the breakdown, reinforcing the fact that England's back-row play has for some time been vastly over-rated and their captain Chris Robshaw is decidedly off the pace.

© David Rogers/Getty Images

They also had no counter to Australia's fine midfield kicking game, with Matt Giteau's left boot so crucial to mixing it up; or to the Wallabies' defiant defence, which involved a long line of courageous tackles, often by some of Australia's smaller brigade.

As for Danny Cipriani's brain-dead pre-match comment that "not one Australian would get into that England team right now", it is more a case of "not one Australian would want to get into that England team right now".

Near where the Australian media contingent sat in the Twickenham stands were two former Wallabies- prop Ben Darwin and the country's greatest rugby No 10 Mark Ella. They both took delight in seeing an Australian scrum stand up and a Wallabies No.10 take control of a match and inspire a victory that has completely changed the complexion of this tournament.

With the victory, Australia have emerged as a genuine World Cup threat to New Zealand. A trans-Tasman fixture on the other side of the world to determine who can show off the Webb Ellis trophy on the night of October 31 looms. The All Blacks remain favourites by a considerable margin, but Australia are now more than a mere irritation.

World Cup-winning teams must win the big matches. And Australia-England was a big match with enormous consequences, with the Wallabies having to perform in an intimidating environment.

Matt Giteau dives over to score a try© Mitchell Gunn/Getty Images

That Australia took control of this encounter so early, silencing the England crowd, shows they have at last the self-belief, maturity and killer instinct that takes teams to a higher level.

Even a doomed England coach Stuart Lancaster had to admit that. A clearly devastated Lancaster handled himself well at the media conference, keeping up a level of decorum, even though immediately hit with cutting questions over whether he should consider his position. He had to confess that his team had let the country down.

Stuart Lancaster, Head Coach of England© David Rogers/Getty Images

Then as a reminder that he will soon be a tournament spectator. Lancaster was asked if Australia could win the World Cup.

"On that performance definitely," Lancaster said, explaining how Australia had "world-class players" and that David Pocock "is the best" at the breakdown.

All encouraging news for Australia.

Now here's the big if and but.

Australia's major consistency is their inconsistency. So often they follow inspired performances with absolute poop.

It is crucial for Australia to finish top of Pool A as it will make their course through the finals that much easier. And their final pools opponents - Wales - look vulnerable as they have an endless list of war wounded.

It is a game Australia should win comfortably. But the Wallabies are masters of crashing down the slippery slide. Their coach Cheika is already right onto it, stressing after the England game to the players that they are about to confront the wiliest of opposition coaches in Warren Gatland, and how it would be fatal if they underestimate Wales - even for a split second. He will hammer that theme all week.

Cheika understands the dark side of the Wallabies beast, knowing that another monumental effort is required in a week's time at Twickenham. Anything less will not be good enough. The pressure remains firmly on the Wallabies.