Terms of reference for the public inquiry into the Grenfell Tower fire may not satisfy the government's legal obligations to investigate the full circumstances of the tragedy, lawyers representing some of the victims have warned.

Prime minister Theresa May today accepted retired Court of Appeal judge Sir Martin Moore-Bick's recommended terms of reference for the inquiry into the fire, in which at least 80 people died.

The terms will cover the fire, the building's history, its most recent refurbishment, the state of building and fire regulations, and aspects of the relationship between the tower's residents and the local authority, including the days immediately following the fire. Local and central government response in the days following the fire will also be included.

However, the terms will not cover all matters requested by local residents, such as an examination of social housing policy, Moore-Bick said. 'Secondly, the inclusion of such broad questions within the scope of the inquiry would raise questions of a social, economic and political nature which in my view are not suitable for a judge-led inquiry,' he added.

Jayesh Kunwardia, social housing partner at London firm Hodge Jones & Allen, which represents some of the victims, said it was 'particularly disappointing' that broader social questions and the adequacy of present housing standards will not be included.

Moore-Bick received more than 550 written responses to his proposed terms of reference.

In its response, HJA suggested terms include the adequacy of steps taken by central government to assess the immediate and long-term needs of those directly affected by the fire, including advice on access to legal aid.

The firm said non-means-tested legal aid should be made available to those directly and indirectly affected by the fire to enable them to access advice on: housing; loss of property, loss of home and consequential expenses; the criminal investigation, the inquiry and inquest process; and personal injury and Fatal Accident Act claims.

Jocelyn Cockburn, joint head of civil liberties, said: 'It is seriously in doubt that these terms of reference will satisfy the government's legal obligations to investigate the full circumstances surrounding the Grenfell fire. The chair should not be ruling out issues, at this early stage, which may prove to be relevant to the causes of the disaster, and this is only likely to further undermine the confidence of those affected, in the inquiry.'

The Housing Law Practitioners Association, in its consultation response, also suggested that the inquiry look at wider issues of social housing policy that may have directly or indirectly contributed to the fire.

However, association chair Simon Marciniak, a partner at London firm Miles & Partners, welcomed the the decision to examine the adequacy of the legislation that regulated the construction and design of the building, and the council's response to residents' concerns.

Moore-Bick hopes to hold a preliminary hearing in September and deliver an initial report by Easter next year.