Bereaved family members and survivors have repeatedly raised concerns about the suitability of retired judge Sir Martin Moore-Bick to lead the inquiry and delivered a petition, signed by more than 22,000 people, to Downing Street earlier this month.
Many have expressed concerns that Cambridge-educated Sir Martin, lacks first-hand experience of the complex social and cultural factors that helped shape the disaster.
Kensington MP Emma Dent-Coad has called for him to stand down.
Under the Inquiries Act 2005, only the Prime Minister can authorise a change in the probe's format. In a letter this week, Sir Martin said it would be wrong for him to advise her either way.
Ms May said that additional panel members should not be appointed in order for the first stage of the inquiry to be completed “as quickly as reasonably possible”.
In a letter to Sir Martin, she said she felt the probe already had “the necessary expertise to undertake its work”.
She added: “I am also very conscious of the need for the Inquiry to complete its initial report as quickly as reasonably possible. I therefore consider that additional panel members should not be appointed at this stage.”
The building, owned by Kensington and Chelsea Council, was home to people from a range of different backgrounds and relatives believe that Cambridge-educated Sir Martin may not have the life experience to understand all the issues involved.
The Prime Minister came under fierce attack for her initial response to the attack and was left embarrassed when no fewer than three people were forced to stand down after being appointed to lead the inquiry.
Deborah Coles, director of the charity Inquest which supports families in cases where public bodies could be held accountable for deaths, told The Independent: “This is a disgraceful and wrong-headed decision which sends a message out to the bereaved and survivors that their voices have still not been listened to, even after the hearings last week. The decision to issue this letter when there can be no parliamentary scrutiny and debate in the run up to holidays is deplorable.
“At a time when many feel mistrustful of an Inquiry team that does not represent their lived experience, this will further undermine trust and confidence. The Prime Minister should think again and appoint a panel as soon as possible as the reasons for not doing so as set out in the letter simply don’t stand up to scrutiny.”
Ms Dent Coad said on Twitter: “This inquiry will suffer a crisis of confidence if those in power refuse to engage with the wishes of survivors and the bereaved. I’m calling on the Prime Minister to reverse this decision. I’ll do all I can to see this panel formed.”
Ever since the disaster on 14 June which left 71 people dead and hundreds homeless, fears have been expressed that a public inquiry could be a “whitewash”. More than 160,000 people signed an earlier petition calling for inquests to be held instead.
Others called for a public inquiry, which has the freedom to explore a broader range of issues than an inquiry, with the terms of reference being devised to fit the circumstances of a tragedy.
If for any reason a public inquiry is deemed by the Government to have failed to deal with all issues of relevance to the purposes of an inquest, there can be both a public inquiry and an inquest - as in the case of Hillsborough, the Zeebrugge ferry disaster and the Ladbroke Grove rail crash.
Two days of preliminary procedural hearing took place earlier this month, with Grenfell survivors and relatives threatening to boycott the inquiry – due to begin hearing evidence in the new year - unless they are given a more significant role in the process.
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