Teachers', parents' and children's groups were consulted on aspects of the School Standards and Framework Bill most relevant to parents: home-school agreements, early-years' learning, and exclusion of children.
Respondents reported that the Bill's overall approach failed to do enough to tackle the causes and consequences of exclusion.
Organisations were also worried that the plans did not require local authorities to target resources on the most disadvantaged children.
The issue of home-school agreements prompted concerns that the parents of children most in need of support were least likely to sign up, and that the agreement itself would reflect the views of only the most involved parents.
A briefing paper issued by the think tank said the Bill would only implement a limited part of the Government's agenda.
It said: "The success of the Government's reform of education in the long run will therefore have to be judged against the broader aims set out in Excellence in Schools and delivered through a range of policy measures."