George North celebrates scoring Wales' first try. Photo / Getty Images

Wales head coach Warren Gatland greeted his team's rise to No 1 in the world rankings after beating England 13-6 in Cardiff by saying, "it's just a number, nice for a day", before warning England that if they were to meet again in the World Cup quarter-finals, "it will be a hell of a battle".

England head coach Eddie Jones piled the pressure on Wales' new status by saying: "Well, that makes them favourites for the World Cup."

Wales extended their winning record at home to 11 tests dating back to 2017 with a performance that was full of character after their limp showing at Twickenham six days earlier, inspired by a man-of-the-match display from under-fire first-five Dan Biggar.

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"The boys turned up properly after lacking edge last week," said Gatland. "If we had lost again to England it could potentially have had an impact if we were to meet them in the World Cup quarter-final. The ranking is a nice accolade but we won't be trumpeting it from the roof-tops.

"There will be lots of Kiwi journalists saying that it is a joke," said Gatland.

"But we won't be making a fuss about it. The boys wear this jersey with pride, and if a team is going to beat us they are going to have to play pretty well because these boys are very proud Welshmen who are not going to roll over easily. We showed some big cojones today."

Biggar had been slated by former Wales and Lions wing JJ Williams, who stated that they would never win a World Cup with him in the pivotal position of first-five.

Biggar thanked Williams publicly as he received his man-of-the-match award, noting that the criticism had "motivated" the team.

Wales, who travel to Turkey today for a training camp ahead of back-to-back fixtures against Ireland, have minor injury concerns over James Davies (concussion), Gareth Davies (hip), Biggar (shoulder), Aaron Wainwright and Jake Ball (dead legs).

Jones was not disheartened by England's showing as it furthered their World Cup preparation.

"It was brilliant preparation, a big step forward as we had to see if we could back up last week," said Jones, who has two more warm-ups to go, against Ireland and Italy.

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"The result is the result."

Earlier, Jones said before the All Blacks' win over the Wallabies that Steve Hansen's team were keeping some things up their sleeves and would not be too fazed by a third-place finish in the Rugby Championship.

"The last thing you want to be is flying before the World Cup," he said.

"When you fly, you have to come down. You go into some games [before the tournament] under-prepared. Are you telling me that New Zealand have been going 100 per cent? Look at it historically. Before New Zealand won the last two World Cups, they would go absolutely balls-out in the Tri-Nations.

"They learned that this period is about crafting your players and your game to have the discipline to be able to play in a number of ways.

"When you get to a World Cup, you cannot rely on one approach. You have to be able to adapt and that is what the games in the build-up are for. I am sure that Steve Hansen cares about where they finished, but having seen the way they have played, what I do know is that he is planning for the future."