So, onto next week.

For Wales that is some warm-weather training in Turkey.

For England some slight chillier Blighty-based work-outs ahead of next Saturday's meeting with Ireland.

We will have full reaction from both camps coming up on the website.

See you later.

Richard Wigglesworth, one of the scrum-halves not to make Eddie Jones' Rugby World Cup squad, relished Dan Biggar clapping back at JJ Williams criticism.

In fairness to Williams, he said that Wales wouldn't win a World Cup with Biggar at fly-half. They may well won't.

Wales head coach Warren Gatland said on Channel 4: "It was a proper Test match, it was tough, it was physical. I said to the boys in the changing room, we showed massive character and big cajones. We lost Williams just before kick-off.

"Other teams are going to beat us at some stage, but if you're going to beat us you have to play pretty well.

On not having the Principality crowd at the World Cup: "We've done a pretty good job in trying to win over the support of a lot of Japanese so with us playing in red, they will support us. It's away from home and is going to be a big challenge for all the countries."

David Heggie: Well done Wales, but don't expect a ref that helpful every game.

Dan: I know the World Cup's all that matters, but we've just won the 6N with a Grand Slam, we've lost one game in our last fifteen, including victory over the Rugby Championship Champs, and being #1 in the world is cool.

Craig Ashcroft: Everyone moaning especially non welsh but remember england bored their way to the World Cup.

England captain George Ford said on Channel 4: "It's a disappointing result. I can't fault the effort, the commitment was brilliant again today. We just need to tidy a few areas up - discipline and the breakdown.

"We knew Wales were going to come back. We wanted to play a better game this week too. That was a proper Test match - physical, not much time and space.

"It's been good for us to play in a stadium like this with the roof closed so we'll keep working.

"I don't think many people will remember these games. What happens at the World Cup in a few weeks' time will be completely different so we'll be ready for that."

Image source, Getty Images

Wales captain Alun Wyn Jones: "Satisfied, just. The first half was a definite improvement, for patches in the second we dropped off. Happy with the improvement at the set piece in particular.

"We worked on physicality and being quicker off the mark, we had that today."

On Dan Biggar's performance: "Ten is a position in Wales that has always been in vogue, fair play to Dan he stood up today knowing the pressure was on him at home."

On the world number one spot: "We are a team of 3.3 million so we can be happy with that."

Richie Rees
Former Wales international on BBC Radio Wales

Wrap Dan Biggar in cotton wool. If it were me, I wouldn't see him again in either of the Ireland games.

Jake Ball did particularly well today and Aaron Shingler had an impact when he came on. Wales' scramble defence was excellent.

Criv: For a team ranked number 1 and supposedly best team in the world, Wales look a million miles off the All Blacks!

Paul Williams: Wales fans celebrating like they won something, no one won in that game. Can I have 80mins back please.

International: Like a sloth, Wales work out a win at home. Will this style of rugby win at a World Cup... When has rugby been an indoor sport... In August.

Image source, Reuters

And here is man of the match Dan Biggar: "Delighted to get the win. We were all fully aware we didn't front up last week. It was a huge defensive effort today, we played some good stuff and could've been further ahead in the first half but really pleased to get over the line."

Responding to criticism from JJ Williams during the week: "Special thanks to JJ Williams for his comments this week, it's been really motivating.

"The forwards were brilliant all day - England's strength is in the set piece, to front up and keep a world class team tryless is an excellent effort.

"We go to Turkey for a week to hopefully get better for the two Ireland games."

On becoming world number ones: "We probably got a bit caught up with that last week, the winning run and going for world number one.

"We worked hard today and it's nice to be where we are. It was a huge effort from the lads today."

Garin Jenkins
Former Wales international on BBC Radio Wales

We talked about Anscombe being out before the game, but it was Biggar's individual decision making which changed the course of that game.

His control was good, his chasing of the ball - he's world-class at retrieving kicks. Biggar has showed his capabilities this afternoon.

Richie Rees
Former Wales international on BBC Radio Wales

Dan Biggar - the experience, the quality and the cohesion he had with players around him. He controlled and dictated the game for Wales. Two moments of brilliance from Dan Biggar effectively won the game for Wales this afternoon.

Gareth Griffiths
BBC Sport Wales at Principality Stadium.

Wales are top of the world rankings officially for the first time after defeating England.

That will be confirmed when World Rugby weekly rankings are officially published on Monday.

They go above New Zealand despite the All Blacks winning 36-0. The best team in the world will be determined after the World Cup final on 2 November. But not a bad accolade to have currently. Dan Biggar man-of-the-match.

Image source, Reuters

Where is that ball?!

It creeps out the back of the ruck on the Welsh side and Jarrod Evans boots it into touch.

That's it. Wales get the win, and the world number one spot!

The atmosphere is really cooking in Cardiff now. A scrum five metres from their own line for Wales as the clock ticks beyond the 80-minute mark...

Huge drive from England, but the maul is taken to the ground and there's an almighty roar around the Principality Stadium. Wales get the decision, and George North pumps his arms into the air in delight.

The hosts are almost there...

The Daily Mail reporter Will Kelleher here suggesting that Wales might go top of the rankings, but might be short of an All Blacks side that savaged Australia 36-0 earlier today.

Fair shout?

Alun Wyn Jones is penalised for ripping the ball on the floor just outside his own 22 and Owen Farrell wants to get England steaming forward quickly.

Ben Youngs feeds Courtney Lawes and then Jamie George and then Wales are called offside.

England opt for the corner.

So England need a converted try to level things up here. They've not looked like crossing in the opening 77 minutes, mind...

Garin Jenkins
Former Wales international on BBC Radio Wales

That's a great confidence booster for Halfpenny and Wales.