Leicester's Austin Healey flew out to Australia from Heathrow last night as cover for Josh Lewsey and Iain Balshaw, who are both struggling with leg injuries.
But Woodward is predicting that England could be in a position to name their strongest line-up for the first time in the tournament.
He said: "I have spoken to the doctor and I expect to be able name the team from a full strength squad on Wednesday. I'm very confident Richard Hill will be available.
"All the players currently injured should be available to me, especially Hilly. I can say that with confidence because of the change I've seen in his persona and the fact that he has been running around injury free since Friday."
England have so far failed to produce their best rugby and that was partly due to the absence of the irreplaceable Hill, who added: "If there had been an emergency I would have been able to play in yesterday's quarter-final.
"I'm really looking forward to getting on the pitch."
Woodward insisted that England would raise their game once "we get to put out our strongest XV".
He said: "We're not at our best yet but on form we deserve to be here and we now need to move up a gear.
"We haven't come here to be second or third - we've come here to win it."
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