Australia and Wales occupy the top two places in Pool A with 13 points each after Saturday's game, leaving England trailing in third place on six points with one pool match remaining.
It was Australia’s highest score and biggest margin of victory over England at Twickenham, where they won the first of their two World Cups by beating the English in the 1991 final.
The Wallabies will play Wales at Twickenham for top spot in the pool before England close their tournament against makeweights Uruguay in Manchester next Saturday evening.
England's head coach Stuart Lancaster apologised to the home fans who had packed Twickenham.
"Sorry we let everyone down. The last five or 10 minutes we came up short. We have young players and I hope everyone stays behind them," he said.
Flyhalf Bernard Foley scored two tries and kicked 18 points for Australia, who led 17-3 at halftime, with centre Matt Giteau adding a late third try after wing Anthony Watson had charged over for England.
Australia were too fast and mobile for England at the breakdown and their backs pierced gaps in the defence with smart offloads at pace while the home forwards failed to dominate the Wallabies in the scrum.
England flyhalf Owen Farrell kicked eight points but sat out the end of the match in the sin bin.
Springboks top pool
Earlier in the day Japan lit up the tournament once again with a 26-5 victory over Samoa in Milton Keynes before South Africa went top of Pool B by beating Scotland 34-16 in Newcastle.
Twice world champions South Africa, stunned 34-32 by Japan in their opening match, scored first-half tries through flanker Schalk Burger and wing JP Pietersen, his fourth of the tournament, to lead 20-3 at halftime.
Scotland rallied to make the Springboks work hard for a win that was completed by Bryan Habana's 61st test try, a Springboks' record, after Tommy Seymour had pulled one back for the Scots.
Japan, who had won only one match in 24 at previous tournaments, made Samoa pay for indiscipline that resulted in three players being sent to the sin bin during the match.
Fullback Ayumu Goromaru kicked four penalties and two conversions for a 16-point haul to become the tournament's top scorer with 45 points and keep alive Japan's hopes of reaching the quarter-finals.
South Africa lead Pool B by one point from the Scots, with Japan two points further back. All three have two wins apiece.
The Springboks and Japan both have remaining matches against the United States, who are bottom with no points, while Scotland face Samoa.
South Africans had more than one reason to celebrate on Saturday, however. The late Nelson Mandela, who memorably handed winning captain Francois Pienaar the William Webb Ellis trophy at the 1995 final, was inducted into the Rugby Hall of Fame before their win in Newcastle.
