Their call follows confirmation from the government earlier this week that the consultation - first announced in July 2015 - is set to open in early 2017.
Over the past 18 months, the rate of children's centres closures and service reductions has increased as a result of deep local authority budget cuts.
In December 2016, government figures showed nearly twice as many children's centres closed in 2015 compared with 2014 - 156 up from 85.
Pre-school Learning Alliance chief executive Neil Leitch said the current situation was neither acceptable nor sustainable.
"It is vital the government moves forward on this issue as a matter of priority," he said.
"Despite an ongoing lack of adequate funding, children's centres remain an invaluable source of support for children and families across the country - particularly those that are the most vulnerable."
He added that the government must ensure children's centres are safeguarded and supported in the long term if it wants to be "serious about social justice".
Action for Children director of policy and campaigns Kate Mulley called on the government to provide "a clear direction about the role that children's centres are playing in local communities to improve the lives of disadvantaged children and deliver their promise to promote social mobility".
"We are eagerly awaiting the children's centres consultation − the futures of thousands of children depend on the vital services provided through them," she said.
"We know local authorities' funding has been reduced, but needs on the ground have not."
Family and Childcare Trust deputy chief executive Ellen Broome echoed her call, asking for the government to provide "a period of stability" by clarifying the core offer local authorities should provide to every family in the early years "and protecting the funding to deliver this offer".
She added that the organisation would like to see the consultation explore whether links between children's centres and early years providers could be promoted "to maximise the reach of early intervention services".
The DfE said the consultation would still go ahead despite the decision to scrap plans to publish a life chances strategy, which was to include the consultation.
Instead the government intends to include elements of the strategy, which was to address child poverty among other issues, in a social justice green paper to be published this year.