Ms Everingham told the seminar, mounted by the voluntary organisation Home-Start UK, that education authorities were required to be involved in devising children services plans, which will become statutory from next month.
The plans were "the key to getting local authorities to think across their departments and their services". Social work alone could not and should not provide support.
Early intervention was essential to effective action. Social work departments would "identify at an early stage those who will present difficulties in future to all departments". Action, Ms Everingham suggested, could include ensuring that children were placed in an educational setting where they could realise their potential.
Margaret Harris, director of Home-Start, which links volunteer befrienders with vulnerable families, said relatively small sums for voluntary organisations could lead to "vibrant local schemes".
Zoe Dunhill, medical director of Edinburgh Sick Children's Trust and a consultant paediatrician, said early intervention should begin with the under-threes. That did not mean, as Ms Everingham had implied, "noticing difficulties in seven or eight-year-olds".
Marion Macleod, children services manager with Edinburgh social work department, questioned how preventative measures could be brought in when statutory services were "being badly hit".