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The rematch of the 2019 World Cup final rounds off a disappointing year for Eddie Jones' men, who have lost five of their 11 games and also drawn 25-25 with New Zealand in their most recent outing.
The rivals clashed at the same venue in 2021 when England edged a thrilling 27-26 victory, and Cockerill has braced his team for another full frontal assault.
"The Springboks play in a very different way to most other teams," forwards coach Cockerill said.
"They don't vary much. You know what's coming, they're coming through the front door and you have to match that.
"We managed it last year in the same fixture but only just and we have to make sure that whatever happens, when we have periods when we're on top or are under pressure, we have to survive, stay in the game and make sure we convert our pressure into points.
"Against New Zealand, although for the first 70 minutes we were under huge pressure in parts, we hung on and we stayed in it.
"We have to be very physical and match whatever the Springboks bring and wherever possible try and get dominance. It's going to be tough but it's a challenge we've got to go at.
"We felt we were a little bit off in the set-piece at some parts against New Zealand and there's no greater challenge on that front than what we're facing in South Africa."
England are aiming to go toe to toe with the 'Bomb Squad', the Springboks' front row replacements who left a major dent on opponents at the World Cup three years ago.
Mako Vunipola, Jamie George and Kyle Sinckler start to reprise the rolls they performed in Yokohama in 2019 with Ellis Genge, Luke Cowan-Dickie and Will Stuart scheduled to arrive as third-quarter reinforcements.
"My attitude to the Bomb Squad is that it's a narrative they like to create. Our three lads on the bench don't think they're inferior to what they've got," Cockerill said.
"When they bring their front row on and when we bring the finishers on in Genge, Luke and Will, we're looking forward to rolling our sleeves up and getting into it. They know what they need to do.
"When I look at the starting front row and look at the bench, they are two very, very good front rows.
"That's a very combative starting three and that energy and aggression off the bench is something that I'm looking forward to seeing."
England have been under pressure this autumn from the moment they lost the opener against Argentina but a victory over South Africa would rescue the campaign from failure.
"We want to win but it's not the end of the world if we don't and we've not solved all our problems if we do," Cockerill said.
"It will be a good way to finish the year leading into the Six Nations. Of course it's good to win so that we can keep building. We have to keep learning our lessons.
"We learned our lessons against New Zealand and now we need a much improved physical performance, especially from the forward pack, to make sure we do what we want to do."
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