Survivors and the bereaved of the Grenfell Tower disaster want next week’s public inquiry report to be as hard-hitting as the Macpherson report on the murder of Stephen Lawrence, but instead fear it will be an establishment fudge drowned out by Brexit.

Several have told the Guardian they want the first official conclusions about the 2017 fire, which killed 72 of their neighbours and loved ones, to strongly criticise the leadership of the London fire brigade, rule that the refurbishment with combustible cladding was illegal and call for a stay-put policies to be abandoned.

But they fear that the inquiry chairman, Sir Martin Moore-Bick, a retired high court judge, could go soft on the authorities, stop short of concluding that the towers’ residents were victims of “institutional indifference” and defer a ruling on the legality of the council block’s 2016 refit.

“I hope Moore-Bick sees his place in history,” said Joe Delaney, a resident of the Lancaster West estate who witnessed people falling from the building. “I wouldn’t want to be remembered as Lord Hutton [whose 2003 inquiry clearing the government of wrongdoing over the death of the Iraq war scientist David Kelly was widely criticised as a whitewash].

“I would rather be remembered as Macpherson. But from what I have seen of him, he has the tendency to go on the side of caution and the establishment.”

On Monday, hundreds of core participants in the inquiry will be granted a preview of Moore-Bick’s much-delayed report on what happened on the night of the fire. The report is due to be released on Wednesday.

A second inquiry phase examining the refurbishment begins in early 2020 and is not expected to report back until at least 2021, leaving many fearing next week will not bring closure. However, the strength of its conclusions could determine the level of trust the survivors feel they should place in the second phase, amid complaints the community has so far been marginalised by the inquiry process.

“It had better be hard-hitting,” said Sandra Ruiz, the aunt of 12-year-old Jessica Urbano Ramirez, who died in the tower after being told by call operators to stay put and await rescue. “Is something like this going to happen again and a little girl is going to stay on the phone for an hour? She was trusting that person on the end of the phone was going to get her out.”

Karim Mussilhy, whose uncle Hesham Rahman, 57, died on the top floor, said: “I hope that Sir Martin is not going to hold back and it is going to contain some strong recommendations and we can then go into phase two feeling more confident than we do now.”

The report’s publication, the day before the UK’s possible exit from the EU, has sparked concern that Downing Street is trying to minimise publicity. The government said Boris Johnson asked Moore-Bick to publish by 30 October at the very latest and that the inquiry chairman chose that date. Moore-Bick told survivors he was disappointed by the timing, implying he had not been allowed the opportunity to publish after the Brexit deadline.

Many survivors see parallels between the way they have been treated and Macpherson’s conclusion that the Metropolitan police exhibited institutional racism in the investigation into the Lawrence murder. Grenfell United, the survivors and bereaved group, has argued that the way they were treated by their council landlord before the fire amounted to “institutional indifference”.

Delaney also said he believed the LFB showed “institutional indifference” by allowing a relatively junior officer to remain in charge of the emergency response for almost an hour. Further indifference was shown by the cuts made to the LFB, mostly from central government, while Boris Johnson was mayor of London, he said.

Last week Doreen Lawrence, Stephen’s mother, said she believed the firefighting response at Grenfell had been affected by racism, claiming: “Had that been a block full of white people in there, they would have done everything to get them out as fast as possible.” This was strongly denied by the LFB, and tens of thousands of people signed a petition urging her to apologise.

During the 2018 inquiry hearings, Imran Khan, a lawyer acting for some of the bereaved and survivors and who previously represented the Lawrence family, said there appeared to be “unconscious or some conscious racism” in the way some firefighters responded. The suggestion was strongly denied by firefighters.

Moore-Bick has previously said a judge-led inquiry is not a suitable vehicle to consider questions of a “social, economic and political nature”. But he is likely to deliver a verdict on the LFB’s strategy, in particular its decision to continue telling people to stay in the building long after it was ablaze from top to bottom.

Mussihly said he believed his uncle might have escaped if he had not been told to stay put by 999 call operators. “He was trusting what he was being told by the emergency services as anybody would and it cost him his life,” he said.

The stay-put policy “effectively failed” at 1.26am, according to Dr Barbara Lane, the inquiry’s fire engineering expert, but the instruction wasn’t changed to evacuate for another 69 minutes. At that time there were 117 occupants remaining in the building. Only 46 escaped.

“Many residents above me were relying on the services to get to them,” said Antonio Roncolato, who was the second-from-last person to escape the building. “I am sure if they had been told to get out, many lives would have been saved.”

Nabil Choucair, who lost his mother, sister, brother-in-law and three nieces in the fire, said: “After what happened, there shouldn’t be a stay-put policy ever … [My family] left it to the last minute. They were under the impression they were going to be rescued. I don’t have very much faith in the inquiry at all.”

Moira Samuels, a spokesperson for the campaign group Justice 4 Grenfell, which has non-financial backing from trade unions including the Fire Brigades Union, predicted that in the absence of conclusions about the refurbishment, Moore-Bick would unfairly deflect blame for the disaster on to firefighters.

“Stay-put was based on containment [of the fire] and if you are not going to discuss why containment was breached, you are deflecting responsibility from powerful organisations, people who make building materials, people responsible for safety,” she said. “We fear that he will not bring that in.”