Sir Christopher Ball, director of learning at the Royal Society of Arts, said compulsion was needed because inadequate parents did not take advantage of nursery education.
Last year, Sir Christopher's Start Right report argued that there were big social and educational benefits from nursery education. He said children should be in nursery classes until they started school at the age of six, rather than five.
His report was studied by Downing Street advisers trying to implement the Prime Minister's promise of nursery education for all four-year-olds
Yesterday, Sir Christopher attacked the Government for ignoring three- year-olds in its plans to issue nursery vouchers, aimed at giving parents greater choice, only to parents of all four-year-olds.
He said: "If the principle of nursery education is as important as we think, it needs to be compulsory."
The present law under which children had to attend school from five to 16 was based on the belief that children of parents who did not value education would not otherwise send them to school, he added
"We know these children are just the ones who most need the socialising attention that education gives them at an early stage."
Parents would not be forced to send their children to nursery school if they could show that they could teach them properly at home.
So the situation for under-fives would be the same as it is for school- age children at present.
Nursery education for all three and four-year-olds would cost about pounds 1bn.