Teaching unions have praised the ambition of the new Children's Plan but warned against overburdening schools.
The plan will see children's services coming together in schools
The National Union of Teachers said the government deserved credit for its courage, but pointed out primary schools' capacity was not limitless.
The National Association of Head Teachers said the planned link-up with health services would enable schools to focus better on the needs of children.
The NASUWT teaching union welcomed the reaffirmation of existing strategies.
Its general secretary Chris Keates said: "Schools will no doubt be able to meet the challenges in the Children's Plan providing that it is recognised that they cannot do this alone.
"Equal pressure and expectation must be applied to all other key players, including parents."
The NUT's Steve Sinnott said primary schools would embrace the plan if they believed they were in the driving seat.
He also welcomed the promise that national tests would be scrapped, if a two-year pilot on tests based on stage rather than age was a success.
"Allowing teachers to use their professional judgement about when a child is ready to sit tests is a no brainer," he added.
'Fractured home lives'
Association of School and College Leaders general secretary John Dunford said the plan placed "tremendous expectations on schools and their leaders".
He said the government must be realistic about how quickly initiatives could be put in place and not try to put a 10-year plan in position in three years.
He added: "Above all, it must be acknowledged that schools' primary responsibility is still to educate children."
The Professional Association of Teachers general secretary Philip Parkin said schools could play a key role in communities and take on a wide range of services.
But he added: "There is a real danger of overburdening schools and allowing their focus to move away from education to social issues."
The Association of Teachers and Lecturers general secretary Mary Bousted welcomed government plans to put children at the heart of policy.
She said: "For too long teachers have been left with little help to deal with the low health esteem and poor behaviour of children who have been mentally and emotionally damaged by their fractured home lives, poor parenting and poverty.
"But unless the government puts in more funding it will fail to meet its target to end child poverty by 2020."
The Children's Commissioner for England, Sir Al Aynsley-Green, said the plan had the potential to create a society where children were more valued, where their interests took centre stage and where there were significant improvements in their well-being.
"We hope to see the plan implemented in full and look forward to working with government, families and organisations to see this vision become reality by 2020."
The Institute of Directors welcomed the plan to place greater emphasis on language learning in primary schools, as is extra help for those really struggling with the basics.
Its director Miles Templeman warned against driving out breadth and variety when reviewing whether to devote more time to teaching writing, reading and mathematics.
Childcare charity the Daycare Trust said the extension of free part-time nursery places to some two-year-olds in deprived areas would give much-needed help to the poorest families.