West Berkshire Council, which was inspected by Ofsted in March, has said the entire authority has to save £20m over the next four years, with almost £11m to be found in 2016/17.
It has said that £300,000 will come from closing four children's centres as part of a "redesign" of services that will involve making greater use of local community venues and working alongside partner organisations and community groups.
The council said it plans to continue to offer popular early childhood services for families but will charge a fee of around £3.50 per session.
"Like many councils, we have to make difficult decisions about how we save money," a consultation document states.
"We can no longer afford to deliver children’s centre services in the traditional way."
“We will stop using four children's centre buildings, but will provide a greater level of outreach, meaning that our services will still be available, using community locations.
“This means that services will be available in local communities and some families will have less distance to travel to access services.
“However, for others the services that they want may be at a different location, which may be less convenient for them.”
Early years services are coming under increasing pressure as councils seek to save money.
An annual survey published by 4Children last month revealed that nearly two thirds of children’s centres in England have had their budget cut this year and 130 are at risk of closure.
The council also plans to reduce provision of short breaks for children with disabilities, saving £345,000.
A further £40,000 will be saved from the £80,000 the council currently provides in funding for primary child and adolescent mental health services. And £100,000 will be saved from spending on educational psychology services.
In July, the council committed to spending £668,000 to address the points that Ofsted raised.