The two countries have met on six previous occasions in World Cups, including two finals.
Here, the PA news agency looks back at those past encounters.
Australia 19 England 6
May 23, 1987
Pool stage, Sydney
— Rugby World Cup (@rugbyworldcup) August 1, 2019
England were beaten in a hard-fought contest after Australia benefited from a controversial refereeing decision. The Wallabies led 6-0 at half-time but England roared back as Mike Harrison finished off a well-worked move in the corner. Australia reclaimed the initiative when David Campese was ruled to have touched down – even though replays showed he clearly did not ground the ball. A further try from Simon Poidevin made the result safe.
England 6 Australia 12
November 2, 1991
England tried to wrongfoot the Australians by playing a more expansive game than they had throughout the rest of the tournament but the change of tactics was not successful. The Wallabies took control late in the first half after a penalty from Michael Lynagh and a Tony Daly try and they did not allow England back in. England could muster just two penalties from Jonathan Webb, although they might have had a try were it not a deliberate knock-on at a critical time by Campese.
England 25 Australia 22
June 11, 1995
Quarter-final, Cape Town
— Rugby World Cup (@rugbyworldcup) April 23, 2019
Rob Andrew landed a dramatic injury-time drop goal as England beat Australia for the first time in the southern hemisphere in a tense encounter. Andrew and Lynagh had matched each other kick for kick throughout landing five penalties and a conversion each while Tony Underwood and Damian Smith traded tries. The decisive moment came with 82 minutes on the clock as England won a crucial line-out and Dewi Morris set up Andrew from 45 metres out.
Australia 17 England 20
November 22, 2003
Jonny Wilkinson kicked England to World Cup glory in a thrilling final with a nerveless drop goal in the final minute of extra time. Lote Tuqiri crossed early for Australia but his fellow rugby league convert Jason Robinson replied for England and three Wilkinson penalties gave England a 14-5 lead. Australia clawed their way back with penalties from Elton Flatley, levelling the scores in the final minute. Further penalties were exchanged in extra time before Wilkinson had the final say.
Australia 10 England 12
October 6, 2007
England ground their way to another tight victory over the Wallabies thanks to four penalties from Wilkinson. A converted Tuqiri try after an early Stirling Mortlock penalty gave Australia a 10-6 half-time lead but England's powerful pack prevented further damage and Wilkinson's kicking proved critical.
England 13 Australia 33
October 3, 2015
Pool stage, Twickenham
England were dumped out of the World Cup before the knock-out stages as a rampant Australia tore them apart at their own headquarters. Australia fly-half Bernard Foley scored all but five of his side's points in an outstanding display which included two tries. Matt Giteau rubbed salt into the wounds with another touchdown late on. England did claim one try through Anthony Watson and Owen Farrell scored seven points but that barely masked the deficiencies in a humiliating performance.