England coach Brian Ashton hailed his side's resilience after their 36-20 win over Tonga sealed a place in the last eight against Australia in Marseille.
Wilkinson is five points short of Gavin Hastings' World Cup scoring record
Beaten by South Africa two weeks ago England have bounced back to win their final two Pool A games.
"Two weeks ago, according to a lot of people, we were down and out in the tournament," said Ashton. "But we're through to the knock-out stages.
"We know we'll have to go up a gear at least next Saturday."
Ashton singled out two-try winger Paul Sackey for special praise.
"He's being doing that for a while but it's great to see him bring it on to the international stage when he gets the opportunity," said Ashton.
"It's not only the work he does when he's put into the clear, I thought he also did some work in some pretty heavy traffic.
"He's a lot stronger than he looks, he can let support players get to him, he tackled well and I thought he had a pretty good all-round game this evening."
England's only injury worry from the match was winger Mark Cueto, who limped off with a hamstring injury.
Cueto told BBC Sport that he would undergo a scan on Saturday, but the 27-year-old said he was optimistic that the injury was not too serious.
Fly-half Jonny Wilkinson admitted England still have plenty of areas to improve on if they are to stand a chance of beating Australia, their opponents from the 2003 World Cup final.
"We did the basics right but it was a tough. It could have gone either way, but we became strong at the end," he said.
"To win by a few points is satisfying - but we've a fair way to go."
Wilkinson notched his 222nd World Cup point at the Parc des Princes and now trails Scotland's Gavin Hastings by five points as the competition's all-time leading scorer with 227.
But the 28-year-old typically refused to dwell on the positive aspects of his own performance.
"I still need to improve, most of the stuff in my head is what I need to improve upon," he added.
Winger Sackey acknowledged England's most promising moves were down to Wilkinson's influence in midfield.
"The decision-making between 10, nine and 12 was spot on, we played our territory game and kept competing," said the Wasps star.
"We soaked up their pressure and got a good result."
Despite a few moments of inspiration, Tonga coach Quddus Fielea admitted his team did not produce a performance worthy of a place in the last eight.
"I think we were our own worst enemy, our execution wasn't what it should have been," he said.
"But at the end of the day the best team won. It was a marvellous last game and best of luck to England for next weekend."