Sadiq Khan has condemned the way survivors of the Grenfell tragedy were treated as “chaotic and inhumane”, in a furious letter to the prime minister.

The London mayor has issued a list of demands to Theresa May detailing concerns about delays in rehousing survivors, potential immigration enforcement against some of those affected and the make-up of the panel investigating the disaster.

He says the government’s handling of the tragedy risks fuelling perception in some quarters that it is “institutionally indifferent to their continued suffering”.

His intervention, which amounts to a call for a wholesale change of approach from government, comes as the inquiry faces calls to consider the role of “institutional racism” in the tragedy. It has already heard a list of serious safety breaches at the tower.

In his letter, sent to No 10 yesterday, Khan writes: “As the families who lost relatives, friends and neighbours embark on the inquiry and attempt to rebuild their lives, they need to know that their government and council have the commitment and expertise required to support them. The treatment they have faced over the past year has been, at best, inconsistent and chaotic; and at worst, inhumane.

“The process of healing and securing justice will take time but more can be done now to support and care for these families, to make their lives more manageable and ensure they are in a position to fully participate in the inquiry.

“The institutional indifference these families have faced in the 12 months since the fire is simply unacceptable. Your government has failed to give the support so clearly required by the local authority as these families experienced repeated failures and broken promises from the government and Royal Borough of Kensington and Chelsea. It has become ever more apparent to me that your government is unwilling to step in and take responsibility for local response efforts.”

Khan calls for communication with the survivors to be improved, for overseas relatives to be allowed to visit the UK to attend the inquiry, and for rehousing efforts to be properly resourced. He says he hasn’t the power to take the measures himself.

He concludes that he sees “no evidence” that the Grenfell recovery effort is a national priority. “The scale of the tragedy and loss of life warrant closer attention and intervention from government,” he writes. “You must take the action that is needed to demonstrate that the authorities who have already failed the people are not institutionally indifferent to their continued suffering.”

The mayor also called for a “more representative decision-making panel” as soon as possible. The government has already announced that it is adding two members to the inquiry panel who have the skills to examine the cultural and community reasons behind the fire. This followed pressure from survivors and the families of victims. However, they will join the panel only for its second phase: examining why the fire happened.

Downing Street strongly disputed the mayor’s criticisms. A spokesman said: “Following the unimaginable tragedy of Grenfell, the government has been working with survivors to support them as they rebuild their lives and to ensure they get the truth and justice they deserve.

“One hundred and ninety-eight of 203 households from Grenfell Tower and Grenfell Walk – 98% of households – have now accepted temporary or permanent accommodation.

“To assist those in need, the government has spent over £46m to support recovery following the Grenfell Tower fire and committed an additional £34m to support Grenfell recovery. We have provided £100,000 to support local businesses, made £3m available for community spaces and allocated £10m for ongoing mental and emotional support.

“The prime minister is committed to helping the people of Grenfell Tower learn the facts about what happened, to see that lessons are learned and justice is done. Phase one of the independent public inquiry is already under way and the prime minister has confirmed that an extra two panel members will be appointed for phase two of the inquiry, to ensure it has the skills and expertise it requires.”