It was a measure of the strides Steven Smith has made that his output at Cardiff – 33 and 33 – was regarded as a victory for England. And it’s an even more telling measure that he has responded immediately and emphatically.

Good players learn from their mistakes. Good players shape games. The best players do both at the same time. And Smith, who lost his No 1 ranking to South Africa’s AB de Villiers after the first Test, is clearly in the mood to win it back at the earliest possible opportunity.

The wisdom after Cardiff was that England had foiled him with their sixth-stump line outside off stump – and there was some truth in it, not least when Smith edged Stuart Broad to Ian Bell in the slips during the second innings.

Australian Steve Smith celebrates after reaching his double century against England at Lord's Cricket Ground

Smith bats as England's Jos Buttler keeps wicket during day two of the 2nd Investec Ashes Test match

But the dismissal also obscured some other truths. In the first innings, Smith had threatened to humiliate Moeen Ali, casually taking him for three boundaries in four balls, and it had needed a freakish tangle of a catch to silly mid-on to bring about his demise.

In the second, Smith and David Warner had briefly raised hopes that Australia might be able to challenge a target of 412. It wasn’t until Broad got him after lunch on the fourth day that England were able to relax.

And yet, had they been offered a Smith double of 33 and 33, they would have jumped naked into the River Taff to guarantee it.

By compiling Australia’s first double-century at Lord’s since Bill Brown in 1938, Smith confirmed his reputation as the game’s most formidable maker of match-defining runs.

Australia batsman Smith hits the ball for four runs as he turns on the style against England at Lord's

Smith gets ready to run following a shot against England at Lord's cricket ground in London on Friday

In his last eight Tests, he has now made six first-innings hundreds, including scores of 162 not out (v India at Adelaide), 192 (v India at Melbourne), 199 (v West Indies in Jamaica) and now this. It is a frightening record – and it could yet drag Australia back into this series.

Just as crucially, Smith answered the technical questions that had been swirling around him ever since the first Test. England were determined to examine the theory that he doesn’t like to have to reach for the ball outside off stump. Smith’s response was to disprove them.

More than a decade ago Sachin Tendulkar made a double-century against Australia at Sydney – and he did so without playing a cover-drive, a shot which had got him into trouble during the first three Tests of the series. It was an innings of superhuman restraint.

In April Smith remarked that Alastair Cook’s team wouldn’t ‘come close’ to Australia in this series

Smith’s effort here did not quite fall into the same class: he couldn’t resist a drive at Ben Stokes on 50, when Bell failed to cling on to a low chance offered at second slip.

But there was something old-school and heroic about his abstinence the rest of the time – an abstinence that only Test cricket can inspire, with its elongated timeframe, its ebb and flow, its room to breathe.

When Smith resumed this morning on 129, he might have thrown caution to the St John’s Wood breeze, having apparently earned the right to do so. Instead, he buckled down again as England did their best to stick to Plan A. Between the start of play and lunch, Smith added just 39.

Joe Root, the player billed as Smith’s head-to-head opponent in this series, eventually got him with the ball

Crucially, though, he was still there, allowing others to bat around him. Even while Stuart Broad chipped away at the other end, Smith infused Australia’s innings with a feeling of inevitability.

Not all England’s players are enamoured of Smith. He suggested in April that Alastair Cook’s team wouldn’t ‘come close’ to Australia in this series, and was happy to twist the knife in Friday night’s press conference, feigning surprise that Cook had persisted with a deep point.