Currently all care leavers are entitled to support from a personal adviser, providing them with practical and emotional support, up to the age of 21.
But through a new duty introduced through the Children and Social Work Act 2017, from 1 April personal adviser support will extend to all carer leavers to age 25.
Last month, the DfE announced it will increase funding to councils by £12m for the period up to 2021 to cover the new responsibility.
However, the Local Government Association has warned that the government is providing only enough funding for 20 per cent of care leavers. This amounts to around 4,700 young people out of an estimated total of more than 23,000.
It added that no extra funding has been provided for councils to offer any of the follow-up support that a young person leaving care might need, such as short-term financial assistance for help with travel, food or bills, to more significant requests for accommodation to prevent someone becoming homeless.
The LGA said the shortfall will have to be met by councils, which could be forced to find the money by cutting provision elsewhere. It said this would only exacerbate pressures on council children's services, which it said already face an estimated funding gap of around £2bn by 2020.
Richard Watts, chair of the LGA's children and young people board, said:
"This is a potentially life-changing initiative that could make a real difference to young people's lives.
"Personal advisers can play a major role in supporting care leavers as they move towards independence and we were fully supportive of the decision to extend this to all care leavers up the age of 25.
"However, we are disappointed that the government will only provide funding for just 20 per cent of eligible care leavers. While not every care leaver will need the support, we expect the number to be much higher than what the government has anticipated.
"This is further compounded by the fact that councils will receive no extra money to provide any of the essential follow-up support a young person might need, whether it's travel or food, or even a roof above their heads.
"It is essential that this is funded properly by government if we are to help improve young people's lives and give them the best start in adulthood."