It is just over two years since Australia beat England 33-13 in London to knock the hosts out of the Rugby World Cup. Since then it has been an entirely different: played five, won five at an average of just under 35 points per game. The squad floored by the Wallabies in 2015 – and England’s starting XV on Saturday contained eight survivors – has bounced back with a vengeance.

As Eddie Jones is well aware, there remains further scope for improvement. But this was a highly significant win psychologically, despite the fact that a record English margin of victory disguised the tightness of the contest. Even New Zealand do not have a more consistent recent record against the Wallabies and, if Samoa are put away this Saturday, England will have won 22 of 23 games under Jones’s stewardship.

As well as enhancing their self-belief it also ensures they remain the world’s second-ranked team, tucked in behind the All Blacks with power to add in 2018. As the lock Joe Launchbury, having enjoyed one of his more satisfying games at this level, said afterwards, the players are convinced there is more to come. “To get to where we want to get to you can’t afford to just sit in the shirt and put out mediocre performances,” the Wasps captain said. “If we want to be the best side we can be, we have to beat these teams around us.”

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On a damp, difficult afternoon England were indeed in a higher gear than they ever managed against Argentina, defensively right up for it and sharper with the ball in hand. Among the great unanswered questions, however, is what would have unfolded had the Wallabies been awarded one or both of the contentious non-tries which, along with the first‑half yellow cards for Michael Hooper and Kurtley Beale, fundamentally shaped the contest.

Imagine if a more experienced and intuitive referee such as Nigel Owens had been in charge or footage of the ball clearly brushing the touchline whitewash had been available before Elliot Daly’s match-turning 54th-minute try. There is every chance Owens would have awarded Marika Koroibete’s try on the basis that Stephen Moore’s obstruction of Chris Robshaw was minimal or, at the very least, pinged England for an earlier offside. Hooper’s disallowed score was also marginal as the flanker made at least some attempt to stop and play himself back into an onside position. Beale’s binning for a supposed deliberate knock-down might have been only a penalty on another day.

All were fractional calls and could easily have gone either way. Rather than being 13-6 ahead with 10 minutes left England could have been 20-6 behind with Michael Cheika purring up in the stands. Would they have scored three tries in the last nine minutes under more pressurised circumstances? If they had done so, it would have been the finish to end them all.

In their five successive wins against Australia under Jones England have scored five first-half tries to the Wallabies’ six. After the interval they have registered 12 tries to Australia’s five. Regardless of a touch of good fortune here or there, England are regularly finishing stronger than their opponents, one of Jones’s non-negotiables.

“We trained to finish that last 20 minutes hard, whether it was the starting guys or the finishing guys,” the head coach confirmed. “You’ve just got to go through New Zealand’s record in the last five or six years; how many Test matches they’ve won in the last 20 minutes. That’s when it counts. You get in the contest in the first 20 and then you win the contest in the last 20.”

The only caveat when a replacement performs as outstandingly as Danny Care, whose deft kicking set up late tries by Jonathan Joseph and Jonny May before he scored one himself, is that maybe England would win games earlier if one or two of them started occasionally. Jamie George, Harry Williams, Sam Simmonds – all have put in enough hard work this autumn to merit a prominent role against Samoa, particularly if Jones, as he probably will, decides to cut his Lions players some slack.

Come the Six Nations, either way, selection will be fascinating. Mike Brown does not need telling that competition in the back three is intensifying, Launchbury is now a successful Test lineout caller and an increasing driving force all round, Courtney Lawes is undroppable, as is Maro Itoje. Billy Vunipola should be back from injury, along with the Lions Ben Te’o, Jack Nowell and Kyle Sinckler. If Lawes or Itoje switches to six, that leaves Robshaw, Sam Underhill and Simmonds competing for one place, with Hughes also rumbling off the bench.

With the whole squad now reassured that their hard training-ground work is paying off – and assuming they address their questionable game management when Australia had men in the sin-bin – their opponents should be wary.

“I think they look very assured in their roles,” Australia’s fly-half, Bernard Foley, said. “They’re a really quality side and they’re second in the world for a reason.” The Wallabies, who have decamped to Scotland without the injured Ned Hanigan (knee) and Adam Coleman (thumb), know England’s golden Cook Cup sequence is not just down to lady luck.

England Watson; May, Joseph, Farrell, Daly; Ford (Slade, 70), Youngs (Care, 70); M Vunipola (Marler, 64) Hartley (capt; George, 57), Cole (Williams, 67), Launchbury. Lawes, Robshaw, Underhill (Itoje, 17), Hughes (Simmonds, 63).

Tries Daly, Joseph, May, Care. Cons Farrell 2. Pens Farrell 2.

Australia Beale; Koroibete, Kuridrani, Kerevi (Hunt, 67), Hodge; Foley, Genia (Phipps, 71); Sio (Robertson, 70), Polota-Nau (Moore, 64), Kepu (Alaalatoa, 67), Simmons, Enever (Philip, 62), Hanigan (McCalman, h-t), Hooper (capt), McMahon (Timani, 79).

Pens Hodge, Foley.

Sin-bin Hooper 33, Beale 40.

Referee B O’Keeffe (NZ). Attendance 81,909.