Mr Woodhead stopped short of calling for a suspension of the curriculum to allow teachers to concentrate on the 3Rs during the life of the current parliament.
But he warned that leaving the review until 2000 - as scheduled - would be too late.
That view leaves two of the Government's main education advisers at odds. The curriculum chief, Nick Tate, said last week that he was "extremely disturbed" by calls to streamline the curriculum further.
Dr Tate said the move would leave British youngsters lagging behind their peers abroad.
And he hinted that the curriculum review in 2000 could do little more than tinker to avoid disrupting schools as they attempt to hit the Government's tough literacy and numeracy targets.
Mr Woodhead, addressing a conference of Buckinghamshire teachers this week, said: "Primary teachers are in an unacceptable position. If the Government is expecting higher standards of literacy and numeracy, then sufficient time must be made available. I believe the review should be brought forward to enable the requirements of the curriculum to be looked at.
"A year ago I would not have dared say that because of the commitment to a moratorium against change. Now the consensus is that it is important to address the question, particularly at key stage 1, and to ensure that the national curriculum Orders are consistent with the Government's aims."
In a reference to the theme of the Wycombe Area Education Alliance's conference, entitled "Just One Chance", Mr Woodhead said the drive towards raising standards had hit a crucial point.
"I would say that this Government also has just one chance to get it right. This is a critical point for the Government. If this new beginning for education does not work, then we will have lost a vitally important opportunity."
Dr Tate, chief executive of the Qualificatio ns and Curriculum Authority, also underscored the importance of the Government's targets as he addressed a conference last week on health and education - but to a different end.
He feared the disruption caused by any major review of the curriculum and set himself firmly against those who wanted it slimmed down. Sir Ron Dearing had already "cut a lot of the fat", he said.
The "overloaded" curriculum has been a continuing bone of contention in schools - particularly in the final years of primary, where one teacher is expected to cover an increasingly advanced curriculum.
But Dr Tate said better management and training were the key.
"The big issue now isn't about breadth but about the most effective deployment of teachers and their expertise. I get extremely disturbed that many people who should know better are ready to demand that the national curriculum for young people be cut back to deal with what is really a management problem," he said.
"We would be increasing the gap between the elementary education children get in this country and in other parts of the world, where contrary to assumptions many have pretty broad and balanced curriculums and not just the basics.