Williamson reportedly claims, in a letter seen by the BBC, that these placements should be "eliminated", and adds that he could not "imagine a circumstance under which a child under the age of 16 should be living in an independent or semi-independent setting".
In the letter sent to council chief executives, he calls for councils to review all placements of looked-after children in unregulated and unregistered provision, but to pay particular attention in relation to under-16s.
The move follows a BBC Newsnight investigation in October, which reported that more than 100 under-16s in England and Wales were living in such settings.
Providing support for children under 16 without being registered is not illegal, but if care is provided by unregistered settings, this could be an offence.
Newsnight has previously reported that the number of looked-after children aged 16 and over living in such accommodation had risen by 70 per cent in a decade.
The homes are not registered or inspected by Ofsted and police have raised concerns that they provide an easy target for gangs looking to recruit vulnerable teenagers.
Williamson's letter also reminds councils that the law requires each child to have an appointed independent reviewing officer (IRO).
The intended role of the IRO is to scrutinise and if necessary challenge the appropriateness of a care placement before a child is moved.
Children's rights charity Article 39 has recently raised doubts over the performance of IROs.
A consultation on changes to children's cases in the family court, which includes proposals for clarifying the IRO role as well as changes to Cafcass involvement in proceedings and special guardianship assessments, closed on 30 September.
The consultation, launched by the Courts and Tribunals Judiciary, has been considering responses from local authorities and social workers.
A Department for Education spokeswoman said: "The Secretary of State has written to the chief executive of every local authority in England, asking them to review all of their placements in unregulated and unregistered provision, paying close attention to any placement of children under 16 and ensuring that independent reviewing officers have been appointed for each child, as required by law."
Article 39 director Carolyne Willow said that a national strategy for children's residential care is "desperately" needed, adding: "This must be an early priority after the election."
In Willow's view, independent advocates should also be part of the placement review process that councils are embarking on at Williamson's request, "to ensure children are heard and their wishes and feelings taken seriously".
She continued: "Where lack of funding is getting in the way, central government must step in to support councils.
"Added to this, the Cafcass route for IROs challenging unsafe or unsatisfactory placements requires an overhaul so it becomes a genuine safeguard."
Judith Blake, who chairs the Local Government Association's children and young people board, said: "The welfare of the children they care for is of the utmost importance to councils, and finding them safe, stable accommodation is a key part of this. It is essential that every council ensures accommodation is appropriate for the children and young people they are placing there.
"However, we are seeing increasing numbers of older children coming into care. These young people are more likely to need accommodation in children's homes, which is placing significant pressure on places and making it increasingly difficult to always find the most suitable option for each young person's needs.
"Funding pressures alongside soaring demand for care are preventing councils from investing in the accommodation and support options at the level they need in order to provide the best and most appropriate help for all children and young people.
"It is vital that the new government works with councils to understand these pressures and provides appropriate funding to ensure the right homes are available for all children, whatever their needs.
"We are also keen to work with them to ensure all settings, including unregulated settings, provide the best quality accommodation for all children."
When asked for clarification of the regulations on placing under 16s in unregistered settings, an Ofsted spokesman said it was a matter for the DfE.