Some 53 per cent of Conservative councillors think such funding cuts make it more difficult for local council's to deliver legally required responsibilities for children and young people.
Meanwhile almost three quarters said that long-term funding for children's services is a major concern.
The survey of 508 Tory councillors in England - carried out by Survation on behalf of Action for Children - also showed that just over a third believe there is a "lack of clear direction and funding" for children's centres and family hubs and support.
Chief executive of Action for Children, Sir Tony Hawkhead, said: "Our findings show the growing fear that the Government is failing in its pledge to give all children the best start in life.
"Nearly a third of children in England - over 200,0000 - have fallen behind by age five, and with one children's centre closing every week, we're deeply concerned struggling families are being abandoned.
"Early years services are one of the key lifelines for families living in poor housing, in financial trouble, with mental health issues and those whose own childhood experiences affect their parenting. These lifeline services are being hollowed out, fragmented and cut, and children are bearing the brunt.
"The Government needs a bold vision that will give direction and provide local authorities with adequate funding to make sure all our children get the best start in life."