Initial plans, unveiled last year, were for practice supervisors and frontline child and family practitioners at 31 volunteer councils to be assessed during a "first phase" rollout between 2017 and 2019, prior to national rollout.
But there were concerns that the plans could potentially destabilise the workforce, and create a two-tier system based on those who had passed the exam and those who had not.
The DfE said the plan is now for phase one to begin from mid-2018 in Bury, Leeds, Manchester, Oldham and Wigan. A second phase, involving up to 20 authorities is then expected to get under way in early 2019.
The DfE has also said it is not imposing time limits on when accreditation will get under way, abandoning its commitment that all child and family social workers would be assessed by 2020 at the latest.
"We will listen to the local authorities with whom we work, to ensure they are ready and have the right structures in place," the government response to the consultation on its original plans states.
The DfE added that accreditation will not be mandatory at this stage, with a decision to be taken on the appropriateness of mandatory assessment "in the future", based on findings from the testing phases.
The government's intention to scale back the rollout was first announced by children's minister Robert Goodwill at the ADCS conference in July.
Writing in the ministerial foreword of the government response, Goodwill said: "We have listened carefully to [the] responses to the consultation. In direct response to [the] feedback, we will be moving forward with our plans to improve specialist child and family social work expertise, in a more measured way than originally planned.
"The changes we have made to our rollout plans are significant. They will see us working with a group of five local authorities to co-create the support and structures needed to successfully embed the standard and the assessment. Live evaluation will be a feature.
"We will monitor workforce impact carefully. Only when we have designed the necessary building blocks for this new system will we move to a second phase, with a more diverse group of local authorities, making adjustments which will take account of local variations.
"Once we have addressed the learning from this phase we will move to national rollout."
Steve Walker, director for children's services at Leeds Council, said: "The National Assessment and Accreditation System has brought a welcome focus on the arrangements that local authorities have in place to set the conditions in which best practice can flourish.
"Leeds' involvement in the accreditation system will provide us with an opportunity to review and strengthen our career development opportunities for social workers and enable us to recruit and retain great social workers, which is what children and young people need and deserve."