Government guidance on how the Adoption Support Fund (ASF) works, and how help can be claimed, has been updated with references to a five working day target for completing reviews removed.
The DfE said the timescale in dealing with applications from councils and regional adoption agencies has been removed due to "an increase in application processing times".
Adoption UK chief executive Sue Armstrong Brown said that the DfE's decision to remove the target is "unwelcome news" for adoptive families in need of support.
"We are already seeing unacceptably high delays in the earlier stages before the applications reach the DfE.
She added: "Having the DfE five-day turnaround was a welcome backstop in a process that is already running too slowly. Removing that now risks further delay so it is very unwelcome."
A DfE commissioned evaluation of the ASF, published in August 2017, reported high levels of demand and a lack of support in the community for families in areas such as cognitive therapy, play and music therapy and parenting skills training.
In October 2016 a cap limiting how much could be claimed at £5,000 per child was introduced.
John Simmonds, director of policy, research and development at CoramBAAF said significant increases in demand since the fund's introduction in 2015 highlights the challenges many families experience as a result of the child's early maltreatment.
"Unfortunately the demand has also resulted in a range of restrictions being placed on the amount available to each family, the type and focus of interventions and now the timescales for decision making," he said.
"This must be a sign of success on the one hand but also a troubling indication of need and the importance of that need being addressed as a priority.
"The big question currently is the government's plan for the fund for the next public spending round - will it continue, will further restrictions be placed on its availability and what will happen to those families whose wellbeing depends on what is currently being made available?"
A DfE spokeswoman said: "Many children and their adoptive families have had their lives transformed by adoption, and we are determined to support them every step of the way.
"Due to a high volume of applications to the Adoption Support Fund, the processes of approvals is taking longer than usual.
"We will continue to work with councils to make sure adoptive families have access to the support they need quickly."
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Figures released in parliament by children's minister Nadhim Zahawi earlier this year revealed a significant increase in successful applications over the last three years. In 2015/16 there were 3,610 successful applications, rising to 7,191 in 2016/17 and to 9,465 in 2017/18.
Zahawi also revealed that the average amount paid out for support had fallen by more than £2,000 within two years.
Under ASF rules when an adoptive family, as well as those caring for a child under a special guardianship order, is assessed as needing support over £5,000 and £2,500 respectively, the amount over those caps should be matched by their council.
Figures obtained by CYPNow earlier this year found that in the 15 months to 5 January 2018 a total of 74 councils had contributed £686,711 under this match-funding arrangement.