The analysis by the Early Intervention Foundation (EIF) also found that the two-year-old offer delivered only "modest" improvement in educational outcomes for children from disadvantaged backgrounds.
The EIF's analysis sought to assess if the policy delivered on its goal of reducing the attainment gap between the poorest children and their more affluent peers.
It examined the attainment gap between children on free school meals and those not on free school meals at the end of their reception year in 2015/16 and 2016/17.
It found that the rate at which the attainment gap has been falling "did not accelerate notably" in 2015/16 and 2016/17, which are the first years in which the effect of the two-year-old offer would be seen.
However, the EIF did find that for every percentage point rise in take up of the offer, the proportion of five-year-olds at a "good level of development" rose between 0.04 to 0.06 percentage points.
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