The Grenfell Tower inquiry has been delayed again so that the government can decide whether evidence given by professionals and company executives could also be used to mount criminal prosecutions against them.

Hearings were first postponed last week and now will not restart until at least 24 February after the inquiry asked the attorney general, Geoffrey Cox, to promise those involved in the disastrous refurbishment that what they say under cross-examination will not be used to try to send them to jail.

The undertaking was requested by lawyers for corporate witnesses in the public inquiry who were involved in the refurbishment of the west London council block where a blaze claimed 72 lives.

They include the cladding contractor, Harley Facades, current and former employees of the main contractor, Rydon, the client, Kensington and Chelsea Tenant Management Organisation, and the architects, Studio E. They have all threatened to refuse to answer questions otherwise.

Detectives are investigating possible crimes including gross negligence manslaughter but have said they will not send any files to prosecutors until the end of the inquiry.

The inquiry chairman, Sir Martin Moore-Bick, said he understood that survivors and bereaved might be “indignant” that witnesses should be allowed to dictate the terms on which they answered questions, but he said the right not to self-incriminate was enshrined in English law.

The request for the undertaking had been opposed by the bereaved and survivors represented by Michael Mansfield QC, who said it had “caused immense anxiety, distress and anger”.

Mansfield argued that the inquiry already had enough documentary evidence to piece together what happened, but Moore-Bick said the inquiry wanted a deeper understanding of what went wrong at Grenfell and that could only be achieved through cross-examination.

“It will not be possible for the inquiry properly to fulfil its terms of reference if witnesses do not have an assurance that the answers they give to questions will not be used in furtherance of criminal proceedings against them,” he said.

But he added: “It is very regrettable, in our view, that the position likely to be adopted by the witnesses was not made clear months ago when the consequences could have been debated without the disruption to the timetable.”

He said he would urge the attorney general to make a rapid decision because the inquiry was “concerned with matters that directly affect the safety of the public at large”. He said: “The work of the inquiry should not be delayed longer than necessary.”

Hearings were already scheduled to last until summer 2021 and further delays would threaten to push back the inquiry’s final conclusions on the June 2017 disaster until 2022. Costs to the public purse, which have already reached £40m, would also increase.

Moore-Bick said: “Contrary to reports in the press, it does not grant anyone immunity from prosecution. It does not apply to any statements or documents already in the possession of the inquiry and it does not prevent the prosecuting authorities from making use of answers given by one witness in furtherance of proceedings against another.”

The Royal Borough of Kensington and Chelsea was almost alone among corporate participants in saying it wanted its present and former employees to give evidence openly without claiming privilege.

However, John Hoban, a building control officer at the council responsible for overseeing Grenfell Tower’s compliance with building regulations, said he would not answer some questions without the undertaking.

The inquiry has already found that the building failed to meet building regulations, and the Royal Borough of Kensington and Chelsea has apologised for its failures.