Firms involved in the refurbishment of Grenfell Tower have asked for immunity from prosecution before appearing at the new phase of the inquiry.
They want a guarantee from Attorney-General Geoffrey Cox that they will be protected when they give evidence.
The 2017 disaster killed 72 people.
The inquiry’s second phase, which began on Monday, is looking at how the building came to be covered in flammable cladding during its refurbishment between 2012 and 2016.
Experts have previously said the work failed to meet building regulations.
Representatives from organisations including cladding company Harley Facades, building contractor Rydon and the Kensington and Chelsea Tenant Management Organisation are due to appear on Thursday.
The requests for immunity were read out by inquiry chairman Sir Martin Moore-Bick at the hearing in London.
They were met with groans from survivors and families of the victims in the room, who are likely to strongly oppose the move.
Sir Martin told the inquiry: “This development has caused me a little surprise because hitherto there has been the fullest cooperation within the inquiry.”
Under the Inquiries Act 2005, people giving evidence at an inquiry have the right to withhold information which might incriminate them.
An agreement not to prosecute would protect them if they did give incriminating evidence.
The first part of the Grenfell Inquiry examined events that took place on the night.
It found the cladding was the “principal” reason for the rapid and “profoundly shocking” spread of the fire at the 25-storey building.
It also concluded that “many more lives” could have been saved if the advice to residents to “stay put” had been abandoned earlier.
At the opening of the second phase on Monday, the inquiry heard that – with the “sole exception” of the Royal Borough of Kensington and Chelsea (RBKC), which accepted that the refurbishment should not have been signed off – all organisations involved in the work had denied responsibility for the fire in “carefully crafted statements”.
The following day, emails disclosed to the inquiry suggested that companies knew a planned cladding system would fail in the event of a fire.
On Wednesday, the counsel for RBKC told the inquiry it “apologises unreservedly” for “a number of failings” by its building control services during the refurbishment of the tower.
The inquiry heard earlier this week that building control officials failed to ask for comprehensive details of the project including materials used in the cladding system.