Vunipola was set to miss the climax to Pool C against France last Saturday only for the game to be cancelled because of Super Typhoon Hagibis, and was also considered a doubt for the last-eight showdown.

Jones names his team to face the Wallabies on Thursday and Vunipola, the only player to have started all 12 of England’s Tests this year, will be an automatic selection if fit.

“Billy is progressing really well,” defence coach John Mitchell said.

“He has trained again today and we are very confident in his progression each day. He’s very likely (to be available).

“Billy is a very important player to us and a very likeable player as well. He fits well within the team.

“He loves the ball in his hand. He is very good at regaining and retaining momentum. He likes carrying the ball which is where he has his greatest influence.”

While the update over Vunipola has been positive, it appears increasingly unlikely that wing Jack Nowell will play any part in the quarter-final, with Jonathan Joseph in line to take his place on the bench.

Having recovered from ankle surgery and the removal of his appendix, Nowell’s comeback against the Pumas came at the cost of a hamstring injury that has prevented him from taking a full part in training.

“Jack wasn’t at training today. He is on another prescription of training and is also progressing,” Mitchell said.

England are odds-on favourites to complete a seventh successive victory over Australia under Jones, but their old rivals will enter the match in a more battle-hardened state.

Compared to the comfortable passage through Pool C enjoyed by the 2003 champions, including the abandoned match against France, the Wallabies have been fully tested by Fiji and Wales.

They have gone into decline after reaching the last World Cup final, but Mitchell insists they remain the game’s great innovators in attack.

“The first thing that we acknowledge is that Australia are a very clever football team. They are always clever and always have the ability to surprise,” Mitchell said.

They love ball in their hands, which is something they thrive on. They have always been highly intellectual in the way that they play and that is something that I respect.

“Clearly, we are going to have some really excellent width in our defence because they love to play both sides of the ruck.

“All you want as a defensive team is to be tested and defence is very important to us and something we enjoy, so we are looking forward to whatever is chucked at us.

“The second thing for us is that we have our own beliefs and our clarity in terms of how we want to play. We are looking to embrace this opportunity.”