Woodward on Thursday confirmed that King was no longer in contention for a place in England's 30-man squad because of a knee injury.
Paul Grayson is now likely to travel to Australia as Jonny Wilkinson's main understudy.
Woodward said: "On behalf of the squad I wish Alex a speedy recovery. He will be looked after by the England and London Wasps medical teams and see a knee specialist to ascertain how long he will be out for.
"However, it is certain that the knee injury precludes him from our thoughts for the Rugby World Cup, but he has made a huge contribution to our preparations for it and if his recovery goes well he may be in a position to be on stand by during the tournament."
King's injury also throws a lifeline to Dave Walder of the Newcastle Falcons, who was one of eight players cut from the squad on Monday, and Leicester utility back Austin Healey, who failed to make the bench for Saturday's game against France at Twickenham.
Woodward also announced that the veteran Lions, England and Bath centre Mike Catt would be carrying out some conditioning work and fitness tests at Pennyhill Park.
"Mike will be with us for today [Thursday] only for some fitness tests and to have the standard medical checks," said the England coach about Catt – who last played Test rugby against South Africa on November 24, 2001.
"It [playing Test rugby] would be a tall order and I haven't picked him. We've just got to make sure all our options are covered. I've been talking to Catty daily and I've preferred him to stay at his club and play as many games as possible. I got the tape of his game against Exeter yesterday [Wednesday] and he looked in great shape and played well.
"With Alex now being unavailable it is important that our medical staff do their full assessment before I name the 30 players and the non-travelling reserves on Monday."
The position of reserve fly-half has caused Woodward the biggest headache of late. Since the injury to Sale star Charlie Hodgson during the Six Nations, Woodward has explored various options.
Experiments with Walder were precluded after he too succumbed to a long-term injury from which he has just recovered. Healey – who plays fly-half on a regular basis with Lecisester – has long made it known he would like to be regarded as a potential England No.10, but Woodward has made scant use of his talents in this crucial position.
An example of this was Healey's selection at scrum-half against France in Marseille last week.