Hill, 27, scored a crucial try in the second half of the 21-13 victory at the Principality Stadium before limping off in the closing stages.
Wales head coach Warren Gatlland. "It'll be quite interesting who plays in the last few games but it's sad for Cory".
"He's certainly going to be a loss but any loss is someone else's opportunity", said Wales skill coach Neil Jenkins.
Gatland amplified England's misery by declaring "when it's really mattered, I've questioned whether they can win these big games" as a World Cup year took a fascinating twist.
"We went through some pain in terms of how hard we trained", he said.
The win was also the 12th successive victory for Warren Gatland's side after they finished the summer and autumn internationals a year ago undefeated while registering victories over France, Italy and now England in the ongoing Six Nations tournament.
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Meanwhile Woodward urged officials to shorten the length of the Six Nations, arguing Saturday's match should have been played a week earlier.
After two weeks on the road - and two opening wins - Gatland was happy to be back at their Vale Resort base west of Cardiff to prepare for the Six Nations rugby showdown with England.
"We'll have a couple days off, lick our wounds, see who is available and get ready for Italy".
'We can't get the added extras now but we can still win the Six Nations.' Kyle Sinckler's lack of discipline was highlighted after the match. England said they were coming down to spoil our party and perhaps we have spoiled theirs.
"The people we had and the people who came on today stood up".
"We certainly had to up our game from the first two (against France and Italy), and I think we did that".
England continued to show their pace, power and class as Breach finished off a flowing move out wide, Packer crossed off the back of a driving maul, and then Bern showed some fancy footwork and acceleration to go over for her second and the bonus-point inside half an hour. Perhaps it was a bigger game for us because if they had won they would have gone on to win the championship comfortably and I was glad to make a contribution.