Research conducted by the Family and Childcare Trust (Fact), based on focus groups and surveys with more than 460 parents found that "many parents found it difficult to access good quality services".
It also found that, while many parents found it easy to access local services, some reported that online information was not always up to date, and parents often reported that they had not used a service locally because they did not know it was available.
Fact is calling on government to publish a comprehensive strategy on its approach to family support in the early years, that considers "the full range of ways that support can be provided to families, including children's centres".
It said the strategy should ensure adequate central government investment in early years services with earmarked funding for local authorities.
It also wants parents to be involved with the development of the national strategy, a prioritisation of efforts to strengthen communities, including enabling parents to provide peer-to-peer support for each other, and better local information about services on offer and the potential benefits for them and their families.
The call comes amid continuing cuts to early years services at local level.
Analysis by CYP Now earlier this year revealed there had been a reduction of more than 1,000 official children's centres in England over the last seven years, with 2,501 as of February 2017, compared with 3,631 in 2010.
The government had been due to run a consultation on the future of children's centres, which was first announced in 2015, but is yet to happen.
Ellen Broomé, chief executive of Fact, said: "Parents have made it clear how valuable early years services are to their families. We need these services to be prioritised to support families and social mobility.
Neil Leitch, chief executive of the Pre-school Learning Alliance said his organisation shares Fact's concerns about ongoing reductions in family support and early help services.
"We know that children's centres provide a vital service to both children and parents, and particularly those families from more disadvantaged backgrounds - and yet, over recent years, we've seen a continued decline in the number of children's centres as a direct result of funding cuts," he said.
"Add to this the fact that children's centre inspections have been on hold for two years now, with no sign of any plans to restart them, and it's clear that these services are being unacceptably neglected.
"If the government is serious about improving social mobility, it simply must invest what's needed - otherwise it is those children and families that most need support who will pay the price."