A nationwide inquiry into grooming gangs must “consider the role of ethnicity, religion and other cultural factors”, the opposition leader, Kemi Badenoch, has said.

The government has faced criticism over its efforts to set up the inquiry, which has been subject to delays and rows about its scope.

Speaking at a press conference in central London, Kemi Badenoch said: “I want to be clear that a national inquiry must leave no stone unturned. It must investigate councils, the police and even the government if necessary.

“It must be time-limited, and it must consider the role of ethnicity, religion and other cultural factors.

“Baroness (Louise) Casey’s own report admitted that many of these cases are committed by people of Asian and Pakistani ethnicities. Her own report said that those who downplay the ethnicity of perpetrators are continuing to let down society, local communities and the victims. We agree.

“As I said, I have spoken to many survivors. We are speaking on their behalf. Their lives and their families’ lives have been turned upside down, so separate to this inquiry, the government must act now to ensure that they and their families are supported so they can heal.”

The shadow home secretary, Chris Philp, urged ministers to adopt draft terms of reference for the inquiry drawn up by the Conservatives with help from some victims and survivors of abuse.

The Tories’ terms would ensure the investigation examines the ethnicity and religious background of grooming gangs, place a two-year time limit on the inquiry, and focus it on non-familiar abuse.

The government’s efforts to establish a national inquiry have stalled since the prime minister, Keir Starmer, announced the investigation in June.

In October, the final two candidates to chair the inquiry dropped out of the process amid a row over their connections to the police and social services.

A group of women quit the inquiry’s victim liaison panel, accusing the government of attempting to widen its remit to consider other forms of child sexual abuse.

Ministers brought in the Whitehall troubleshooter Lady Casey to assist with setting up the inquiry, but acknowledged that it could be “months” before a chair was appointed.

Philp said the Conservatives’ terms of reference would set “a two-year time limit on this inquiry”.

“It can’t drag on for years and years,” he added.