Oxfordshire County Council, which is facing additional cuts to its budget, says it is likely that it will have to close some of its 45 children’s centres next year.
The council said that no decisions have been made about how many children’s centres would close or which ones.
However, it is thought that the two children's centres in Witney, the Prime Minister's constituency, are among the centres at risk.
A spokesperson for the council said, ‘Following recent national announcements about future funding for local government, we are now facing the heavy burden of an additional £61m of cuts.
‘We are therefore looking at a real change of focus and emphasis for children’s centres looking to the future.
‘We will not be able to afford the widespread coverage that exists at present with 45 children’s centres. We must therefore concentrate closely on where these services would best be focused for the most vulnerable.
‘The children’s centres have provided valued help and support for families from all backgrounds and we regret having to look at this service in terms of having to make savings.’
The council's budget proposals will be published in December. A decision about the children’s centres will be taken in February.
The move follows a consultation with parents between July and September into the future delivery of the children’s centres.
Sue Richards, a retired midwife who runs the baby cafe at the North Abingdon Children's Centre, said, 'Through the baby cafe we are able to identify vulnerable families early on, who are already comfortable attending the centre, and get them the support they need. If the children's centre closes and early intervention is cut we will end up with more children in Oxfordshire in crisis. This is financially short-sighted.'
She added, 'Families in need are being moved from Oxford City into outside areas such as Abingdon. If the proposals to close the children's centres go ahead they will be left with no support.'