A return to project work and less testing could help motivate children, according to the Social Market Foundation think tank.
A seminar this week considered how primary schools could best build on changes to pre-school education.
The pro-free market think tank has suggested that experimenting with class arrangements, from large group lectures to one-to-one work, could help. Another idea is to drop subjects and to teach children through projects.
Labour introduced free part-time nursery education for four-year-olds in 1998 which was extended to all three-year-olds in 2004. In 2005, 98 per cent of three and four-year-olds took up their free place.
The move followed research showing that early education can help improve a child's social and academic skills, but the SMF is concerned with what happens next. Claudia Wood, research fellow at the SMF, said: "Children can lose those early academic and social advantages during primary school - this is particularly the case for disadvantaged kids. We want to look at how to add value to the primary curriculum so that deprived children can keep up with their peers."
The SMF report is due to be published next month.