Eddie Jones has been mocked up as a clown in the Australian press as the war of words between the England coach and his Wallabies counterpart, Michael Cheika, continues.

Jones has received the same treatment as Cheika was afforded by the New Zealand press during the Rugby Championship – and Warren Gatland following his remarks about All Blacks supporters – having earlier this week been accused of tarnishing his legacy with his “vitriolic” comments about the Australian media during the England’s series whitewash in June.

Cheika was infuriated when he was depicted as a clown by the New Zealand Herald and on its sport front page on Saturday, under the banner, “Introducing the real clown of rugby” The Australian newspaper has splashed a cartoon of Jones as a clown.

Before England’s 3-0 series win in June Jones spoke of “coordinated” plan to help the Wallabies win the first Test and he was incensed by Fox Sports’ Stephen Hoiles, whose lines of post-match questioning were laced with sexual innuendo, and accused the Australian broadcaster of a “disgusting and demeaning” promotional video in the buildup to the first Test.

Cheika responded by saying: “There was a lot of vitriol about Australia – his home nation where he coached and where his opportunities were given to him to catch and grow up as a coach and play. Personally, if you’re looking to leave a legacy somewhere, you don’t want to hit back at it, do you?”, and then launched his own broadside at England’s scrummaging.

Cheika denied England were disrespected by the Australian media during their summer tour and accused Jones of having a manufactured chip on his shoulder before Saturday’s clash at Twickenham.

On Friday Jones hit back: “It doesn’t worry me at all. If Cheika chooses to say that, then it’s his choice. Everyone makes a choice in life about what they say and how they behave. If that’s how he wants to behave, that’s entirely up to him.

“We are comfortable how we have behaved and comfortable how we have represented rugby.

“Rugby is a respectful game and we represent all the kids playing rugby, supporters, and we want to behave in a respectful way. We have to keep the game in its proper state. The great games of the world – golf, tennis and rugby – stand alone because they have standards of behaviour.”

The coaches have seized every opportunity to continue their verbal jousting since Jones renewed hostilities after last England’s victory over Argentina last Saturday by questioning the legality of the Wallabies’ scrum.

“Eddie has always operated with a chip on his shoulder and now there isn’t a chip and things are going well he’s got to keep looking for one,” Cheika said on Thursday.

“He is very respected in Australia, I don’t know where that comes from, the disrespect. He is just geeing up. He is a good Australian coach who took Australia to a World Cup final when we didn’t expect to go fantastic.

“He is respected for that, he certainly is by me as a former team-mate and I think you saw when he was in Australia that he got a lot of respect.”

Glen Ella, the former Wallabies full-back who served as a skills coach for the duration of England’s tour to Australia, also found himself in Cheika’s crosshairs after he claimed the coach is still having nightmares caused by the defeats in Brisbane, Melbourne and Sydney.

“It’s funny, everyone is up the front of the bus when they have had a win,” Cheika said. “A guy like Glen in particular is always up the front for a handout when he has had a win but when it is tough and you have to run uphill I have not seen that bloke or a few of those blokes around.

“I don’t think Glen is working with England any more, so any Aussie who would support England against Australia, especially a guy who has played for the Wallabies, there’s got to be a reason why.

“’I don’t know if he’s bitter. Maybe they want to get us kicked out and have a job there, I’m not sure. He has to have a reason.”