Home secretary Theresa May is coming under new pressure to redraft the terms of the independent inquiry into child abuse so that it has powers to compel witnesses to give evidence and see those who give false statements prosecuted.

The potentially huge shift in the scope and the nature of the inquiry, hinted at by government-appointed lawyers to the inquiry when they met survivors of abuse on Friday, would go some way to addressing concerns that it will be little more than a whitewash.

The current inquiry has been plunged into chaos after its second chair, Fiona Woolf, resigned on Friday after accepting that abuse survivors had lost confidence in her ability to conduct the investigation impartially. Her resignation followed concerns over her links with the former home secretary, Lord Brittan, who has been accused of failing to act on a dossier of paedophile allegations in the 1980s. Woolf’s departure was a huge blow for the government after the inquiry’s previous chair, Baroness Butler-Sloss, also quit.

The former attorney general, Dominic Grieve MP, said on Saturday that May might need to look abroad for someone to chair the inquiry into historical child sex abuse, in order for the victims to have full confidence that it is independent of the British establishment.

Grieve, who left the government this summer, said: “What has happened is very unfortunate, and with the benefit of hindsight I think that we undoubtedly need to find an independent figure.

“It may be that the best way of doing that is to go abroad to one of the Commonwealth countries that has a similar justice system to our own.”

The current inquiry, which critics say is little more than a review of previous investigations, is not being conducted on a statutory footing, which means it is not backed by the full force of the law. Several previous non-statutory inquiries into abuse have been unable to call key witnesses, and this has resulted in survivors feeling that justice had not been served.

Counsel for the inquiry Ben Emmerson QC met survivors of abuse on Friday as the government tried to win back their confidence.

Alison Millar, a solicitor with the law firm Leigh Day, who is representing almost 50 survivors, said that they wanted the inquiry to be given new powers to compel the production of documents and the attendance of witnesses, as well as to ensure that anyone who gives false evidence will face criminal sanctions.

“In order for the inquiry to be able to require documents and witnesses, it will need to be put on a statutory footing,” Millar said. “We were quite encouraged by the fact that counsel for the inquiry very much heard the unanimous view of those at meeting – that the inquiry should be put on a statutory footing. He said that their views would be heard by the powers that be: the Home Office.”

However, Peter Saunders, chief executive of the National Association of People Abused in Childhood, said he was not optimistic that the government would listen to survivors.

“The whole thing is a farce,” Saunders said. “And we are talking about an inquiry that is supposed to be looking at the worst kind of violations, of children. I think it is a dead duck.”

Millar said some of her clients wanted the government to base the inquiry on the Australian Royal Commission (ARC) on institutional abuse.

The ARC conducted a scoping exercise among survivors’ groups and asked them what should be in the terms of reference before the inquiry was launched. Those who gave evidence were automatically offered counselling.

Some legal experts believe a royal commission would also allow the inquiry to move beyond its current geographic remit – it is currently confined to England and Wales – so that it incorporates Northern Ireland, the Channel Islands and Scotland.

Millar said one of her clients had given evidence to the ARC by Skype and that this use of technology could be used in the independent inquiry in England and Wales.

“At the moment it’s being suggested that there will be five roadshows or group meetings around the country, but it may not be possible for people to get to those meetings,” Millar said. “I’ve got clients who rarely leave their own homes and might feel quite unsafe participating.”

Keith Vaz MP, chair of the home affairs select committee, said the committee would “consult widely” once a replacement for Woolf was found.

“The home secretary has spoken with me and I have agreed that the committee will conduct a pre-appointment hearing when she has decided on her next nominee for this post,” Vaz said.

“This time we must ensure that the process is open, transparent, robust and vigorous, so that the nominee is able to assure all the stakeholders of their knowledge of the subject matter, their ability to devote sufficient time to it and their fitness for the job.”