The care and education of under-fives is normally provided by private and state nurseries, and childminders. But David Hart, general secretary of the NAHT, said heads were now willing to provide pre-school services such as out-of-hours childcare.
He said: "Many heads believe you can improve the social skills and attainment of children before they arrive in reception and it can have a dramatic impact on standards in the long term.
"People can continue to complain about children coming into school with no social skills and point an accusatory finger at parents, but it is not particularly sensible to point to a problem without devising a solution.
"The NAHT wants to be part of the solution and a lot of members have a great deal of support for providing early education, providing the funding, staffing and management issues can be sorted out.
A lot of heads already provide nursery education, but they do it on a morning or afternoon-only basis. Parents want provision from 8am to 6pm and that is going to be the future."
He said issues to be addressed included the need for capital funds and the complexity of revenue funding for childcare.
Government funding, says the union, is based on each local education authority's early-years plan. It wants authorities to leave it to heads to appoint staff and manage childcare.
The Government has said spending on Sure Start, early education and childcare will rise between 20045 and 20078 by pound;669 million. There will also be 1,700 children's centres in deprived areas by 2008.
Tony Blair, speaking at the NAHT's conference in Cardiff earlier this year, said primary schools would play a crucial part in creating a "nationwide universal early years service for under-fives".
The Effective provision of pre-school education study found that from the age of three, the centres which most benefit children are maintained nursery schools and centres that combine education and childcare.
Children who attend pre-school venues staffed by trained teachers do better socially and intellectually, the study suggests, Stephen Burke, director of campaigning group the Daycare Trust, said: "I think it is very encouraging that headteachers are taking a lead on this.
It makes sense in a lot of ways.
"Primary schools are the focus of their community. They have facilities which can be used the whole year round. Having that continuity of service and care is crucial for younger children and particularly helps parents with children of different ages."