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The blaze resulted in the deaths of 71 people.

Those affected had called for a more diverse panel to be appointed to the inquiry, following concerns over the abilities of current chairman Sir Martin Moore-Bick.

It was turned down in December by Mrs May, who feared the investigation would be hindered by any overhaul.

The Petitions Committee, which oversees petitions sent to the Government, said it would be seeking clarity from Mrs May over the apparent contradictions in her reasoning.

Emma Dent Coad, Labour MP for Kensington, shared a picture of the letter she received from Helen Jones, chairwoman of the Petitions Committee, on Twitter.

It said: “I hope your constituents will be reassured to hear that the Petitions Committee agrees with them that the Government’s response to their petition was inadequate.

“We have written to the Government to ask for a better response.

The Committee was concerned that the response did not set out the Government’s position clearly, saying first that the Prime Minister would consider the question of additional panel members, but then saying that she had decided that no additional appointments should be made.”

The Petitions Committee is a cross-party group of 11 MPs.

The petition itself is titled “Call on PM to take action to build public trust in the Grenfell Tower Inquiry”. It has so far attracted more than 26,000 signatures and won high-profile supporters including Adele.

Karim Mussilhy, whose lost his uncle in the fire and helped launch the campaign, said: “We strongly believe an independent expert panel is the best way to do that and will ensure public and victim confidence in the inquiry.

“We continue to press our goal of 100k signatures, to secure a debate in Parliament.”