England were unbeaten at home for four years and 22 Tests before their 2003 World Cup triumph, a run that included seven wins against the southern hemisphere giants.
In the autumn of 2002, England beat Australia, South Africa and New Zealand in succession to establish themselves as the best team in the world.
And with the same opponents to face over the next three Saturdays at Twickenham, Robshaw said: "We have to step our game up. We know over the next couple of weeks it is going to get harder and harder.
"For myself and a lot of players, it will be the first time we have played Australia and we are very excited about the challenge.
"The rivalry between England and Australia is brilliant, whether it's cricket or rugby. As players you want to be part of that rivalry.
"I always watch the Ashes when it's on and I grew up watching these autumn international series, watching the big teams coming to Twickenham.
"We always speak about the era leading up to 2003 when it was a fortress, teams came here and didn't get much.
"It takes a long time to create that atmosphere and that aura around the place. Our aim is to have that again."
England easily beat Fiji last weekend, but forwards coach Graham Rowntree also stressed the importance of regular wins over more illustrious opponents.
"We have to start beating these teams," Rowntree said. "The rivalry is there for all of these teams coming up. They are massive challenges.
"To be able to beat a very good and very experienced Australia team would be a significant feather in our cap.
"We are going in the right direction but the proof is in the pudding and it is about time we started beating these teams in the autumn series."
England have enjoyed more success against the Wallabies than against the Springboks or world champions New Zealand in recent years.
Stuart Lancaster's men go into the Cook Cup clash (kick-off 2.30pm) as favourites to complete a third consecutive victory over Australia, who were thumped 33-6 by France last weekend.
The visitors are also beset by injuries, with key flanker David Pocock, centre Pat McCabe and lock Kane Douglas all sidelined, while lock Rob Simmons is suspended.
But England are acutely aware of how the Wallabies responded to a welter of criticism for their Rugby Championship performances, beating Argentina in Rosario - a victory that may have saved coach Robbie Deans his job - and then holding New Zealand to an 18-18 draw in Brisbane a month ago.
Lancaster has steeled his men for a backlash, a message Rowntree reinforced after the squad's final training run at Twickenham on Friday.
"They are a cagey team, a very skilful team," Rowntree said. "You never know where the next threat is coming from so you have to have everything covered. That is what we have found in recent years.
"This is another big step for us this weekend."
England hold the Cook Cup following their 35-18 victory in 2010, when Chris Ashton scored twice and illuminated Twickenham with a sensational length-of-the-field effort.
Such has been the revolution in the England team over the last two years that only four players - Ashton, Dan Cole, Tom Palmer and Toby Flood - remain in the starting XV.
Ashton returns on the right wing after serving a one-match ban, with Charlie Sharples switching to the left, the only change from the seven-try 54-12 win against Fiji last week.
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