He also suggested Jones, the Wallabies’ coach when they lost the 2003 World Cup final to England, was “tarnishing” his legacy in his native Australia because of the “vitriol” he’d displayed during England’s 3-0 series win Down Under in June.

Watch: Eddie Jones interview

Jones, however, again insisted that England had been shown a lack of respect in Australia by a television commercial from host broadcaster Fox Sports that mocked their chances of winning and a bizarre question containing a crude sexual reference from former Wallaby Stephen Hoiles, now a Fox pundit, at a post-match news conference.

“Michael Cheika has had a lot to say this week. I’m disappointed he’s upset,” said Jones.

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“He’s made some comments about legacy, well we don’t have anything to do with legacy. It’s an uncontrollable part of what happens so we’re not perturbed about that.

“We’ll have a cold beer after the game so he’s welcome to join us. I don’t control his emotions.

“We believe that when we went on the Australian tour, [England] staff and players behaved in a very respectful manner.

“But I’ll reinforce again, I found the Australian media very disrespectful so don’t hide away from those comments.”

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Jones added his prematch meeting with referee Jaco Peyper would take place the day before Saturday’s clash, and that Cheika was welcome to join his conversation with the South African.

“We’ve got the green tea set out, ready to go,” Jones said.

Watch: Michael Cheika interview

“We’ve extended an invitation to Cheika, so it will be up to him whether he accepts it or not. I’m not too worried about who is going to attend the party.”

Cheika, speaking later following Australia’s training session at the elite Harrow School in north London, did not seem that keen to take up Jones’s invitation.

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“I don’t know, we’ll wait to see if the referee tells us what time it’s on,” said Cheika.

“Then we’ll decide whether we’re going to go,” added Cheika, whom All Blacks coach Steve Hansen said in June had been “bullied” in the media by Jones during England’s series win in Australia.

“I don’t think there’s anything I can do to influence the referee, so we’re better off just maybe staying quiet and letting them have the meeting themselves.

“I don’t know, I’ll see how I go tomorrow.”

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Cheika insisted he was happy to leave all refereeing questions to Peyper.

“I’m not telling him what to do. He’ll interpret it how he wants,” he added.

“My responsibility is to get my blokes scrummaging right, and square, and doing their best to keep the thing up on its feet.”

Cheika repeated his claim that Jones had attacked Australia’s scrum as a way of diverting attention from England’s set-piece problems.

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“I think he’s done that to take the heat off his own scrum: it’s pretty logical, it’s the oldest trick in the book,” said Cheika.

“At the end of the day what goes on on the field is what’s going to count. But that’s why I’d say he [Jones] has done it.”