The rankings have particular significance this year because the seedings for the Rugby World Cup draw will be based on the standings at the end of the autumn internationals.
England beat Fiji 54-12 last weekend but dropped to fifth after being leapfrogged by France, who thumped the injury-hit Wallabies 33-6 in Paris.
But Stuart Lancaster's men will move above Australia and reclaim a top four place if they win the Cook Cup for a third consecutive occasion.
If France also beat Argentina and South Africa avoid losing to Scotland by 15 points or more, then the Wallabies will drop out of the top four.
But so tight is the competition that a defeat for England by more than 15 points could severely damage their ambitions of being seeded for their home World Cup.
England's remaining autumn internationals are against South Africa, currently ranked second, and world champions New Zealand.
While England are battling to be top seeds when the pool draw is made on December 3 in London, Ireland and Scotland are scrapping for a place in the second band of teams.
Ireland are currently eighth but they will be overtaken by Scotland if Andy Robinson's side can repeat their 2010 victory over the Springboks at Murrayfield.
There is nothing Ireland can do about it after they opted to play Fiji in a non-cap international this weekend rather than a full Test match.
Scotland were in the third band of teams at the 2011 World Cup and failed to reach the quarter-finals for the first time ever after being pooled with Argentina and England.