The cafe outside the Copthorne Tara hotel off Kensington High Street in west London is known informally as Grenfell HQ. Three months since the disaster, around 18 families who escaped from the Grenfell Tower fire are still living in the hotel, and every morning a few of them come to sit here to discuss the increasingly pressing issue of when they will be rehoused.

Only two families who escaped the tower have moved into permanent new homes, despite a firm commitment from Theresa May two days after the fire that everyone would be rehoused within three weeks. Approximately 150 households are still scattered across London in 36 hotels. The hotel bill (excluding meals) already stands at more than £5m.

Grenfell resident Sid-Ali Atmani, who escaped from the 15th floor, is incredulous at the delay. “For three months, people here have been discussing the same subject, every day, every night – housing. It’s making people more and more ill,” he says. The wait has been particularly distressing for his daughter, Hyam, 10, one of about 200 children still in hotels. “She comes back from school to the hotel. She doesn’t have her own kitchen, her own glass. This has been going on for 90 days and 90 nights. She is tired and frustrated.” She found it tough being cooped up in a cramped hotel room throughout the summer holidays. “Some days she sat in the lobby all day. There are a thousand different faces going past. She hasn’t got her toys. This is no normal life.”

The sluggish, chaotic official response to the fire shocked residents in the days after the catastrophe. Kensington MP Emma Dent Coad says things have got worse. She has already dealt with four interim directors of housing seconded to the local council, and says she is so frustrated at the rapidly shifting cast of people meant to be taking charge of the situation that to describe it as “gross incompetence” would be to put a positive spin on things.

“We are constantly being given different people to write to,” says Dent Coad, who was just days into her job as Kensington’s new Labour MP when the fire happened. An emergency Gold Command team was initially in charge, and then a Grenfell Response taskforce, and now the council again. “My head is spinning with all the people who have gone in and are not helping. How can you coordinate things when there’s an ever-changing list of people supposedly in charge, and nobody is in charge of that?”

Sitting in the autumn sunshine outside the Kensington hotel, Atmani says survivors are puzzled by the delay. “Everyone is worried. You feel blind, because you can’t see what is happening inside the Royal Borough of Kensington and Chelsea,” he says, drinking a double espresso to wake himself up; since the fire, he has been unable to sleep well at night.

An older Lebanese woman stops to ask whether he has heard anything new about housing offers. “I don’t know why we’re still here,” she says. “Whenever I see him I ask: ‘When are we going to move from here?’ As if he is the council, and he knows.”

She has not yet been shown any flats to consider. “Every week they say: this week we’ll show you something. This week.” Each family is supposed to have a key worker to help with the process; this woman (who asks not to be named) says her key worker has not been much help. “What can she do for me? Whenever she visits, she asks me: ‘Any news?’ I’m sitting here in the hotel and she is asking me: ‘Any news?’”

As she explains the situation, she tries to stop herself from crying, then gives up. “I’ve no complaint about the hotel; when I leave I’ll write a nice letter to thank them. If I had peace of mind I would stay happily, but we don’t know what’s happening.” She spends most days sitting in the hotel reception, waiting. “Doing nothing. Looking at an iPad, watching cooking programmes, just to keep my mind going.” She minds not being able to open the window in her room or cook her own food, and not having any privacy. But most of all she is troubled by the prolonged uncertainty.

The council and the government both stress the complexity of the process of rehousing the people living in the 151 flats that were lost to the fire. Since many of the Grenfell flats were overcrowded, 196 new homes were needed. Addressing the Commons on 5 September, the communities and local government secretary, Sajid Javid, said he did not “want to see families being forced to move or make snap decisions simply so that I have better numbers to report … What matters to us is not ticking boxes but working at the pace that suits the needs and circumstances of individual residents.”

His position is echoed by the council; a spokesperson emails to say: “We are dealing with severely traumatised people and we do not want to rush anyone to make a decision.”

This frequently repeated line about the council’s desire to treat people gently because they are traumatised, prompts eye-rolling among residents, many of whom say they are desperate to get out of hotels, and that the delay is entirely on the council’s side. A mother of three, who is waiting for permanent housing and who also asks not to be named, joins Atmani at the hotel cafe. “There isn’t a sense of urgency. Things aren’t happening quickly enough. What’s the excuse for the delay?”

Grenfell Tower in the aftermath of the fire on 14 June 2017. Photograph: Dan Kitwood/Getty Images

Most families want to be given a permanent home and are wary of getting into the temporary housing system; many have bitter experience of being on waiting lists for permanent accommodation for years. Many families are worried that the rents, future council tax levels and the tenancy status of new properties may be worse than they had in Grenfell and they no longer trust commitments from the council that all will be fine. After a very slow start, the council has this month begun to show families more properties that they can stay in for the long-term.

Some people have finally been shown flats in the Kensington Row development, where the Corporation of London bought 68 flats for Grenfell families (triggering complaints from prospective neighbours, with one worried that the arrival of social tenants would “degrade things”). The luxuriousness of this part of the development (which was always designated as social housing, in accordance with planning regulations) seems to have been somewhat overstated, and flats bear no relation to those pictured in the media earlier this summer. “The flats are fine, but they shouldn’t have shown people what they’re not getting,” Atmani says.

A former restaurant manager and Sainsbury’s employee, he is energetic, articulate and well able to express his anger. In the past few weeks he has made the prime minister aware of his dissatisfaction with the process during a public meeting, and has fixed up several face-to-face meetings with housing minister Alok Sharma, Home Office minister Nick Hurd, and senior council figures – all to little concrete effect.

Dent Coad is much more worried about those people who are less able to demand their rights. “The provision is completely uneven. Not everyone is articulate; some struggle with English,” she says. She relates an upsetting story about a vulnerable disabled person being left in a hotel room bed without any help. “People are being forgotten about.”

She is scathing about upbeat government statements, accentuating the positive. Javid recently trumpeted the “amazing results” received by Grenfell students who took A-levels and GCSEs after the fire, but Dent Coad remains focused on the less inspirational problems experienced by dozens of residents who have sought her help. One family, whose child was also taking GCSEs on the day of the fire, “arrived at school in underwear; had to be dressed, got through the exams, did not achieve fabulous grades; there was little or no consideration from the school about what had happened and [the child] lost their place at sixth form.” She has worked with the family to find a place for the child in another school, but stresses: “Some people are just managing day to day; they don’t have the energy to fight the big fight.”

Dent Coad is despairing at the lack of progress. “It feels like an arse-covering exercise.”

It is certainly very hard to unpick how much progress has been made. It is a minor thing, but the council press officer (who is otherwise extremely helpful) spends some time on the phone explaining that counting the number of people who have moved into permanent flats is not a “metric” they are using. Puzzlingly, they are listing the higher number who have “accepted permanent accommodation” (but who are still in hotels waiting to move) – currently 18 households. The number who have moved into temporary accommodation is also a metric they release (29 households). He does eventually concede, after we have been going around in circles, that the number of households who have moved into permanent new homes is just two.

Dent Coad is most concerned about the large number of children who remain in hotels. Several Grenfell survivors have sent her pictures of themselves, squeezed together on hotel beds eating takeaway meals. “Some are in rooms next to the parents but not adjoining, so if the children need them in the night they have to go out into the public corridor. There is nowhere for them to do their homework, there’s no sitting room where they can sit and watch telly, nowhere for home-cooked meals, all the things that children rely on for normality at the end of school – they have none of that. It is no way for children to live in a hotel, with different strangers around all the time.”

Rehousing is her immediate priority; next is ensuring survivors are getting proper mental health support. In the longer-term, she wants attention focused on housing inequality. She supports a proposal from Grenfell campaigner Edward Daffarn, who yesterday called for privatised assets to be returned to the community, as reparation for the tragedy. She hopes that whatever money is left over from the £18.9m donated by the public will be ploughed back into the area. “We need to get back the things that have been lost in the last few years, the nurseries, the after-school clubs, the council services that have been decimated since 2010 and put them all back to the service of the community,” she says.

Khalid Ahmed feels uncomfortable walking past the top-hatted doormen in his muddy kit after football training. Photograph: Graeme Robertson/The Guardian

Three miles away from the Copthorne Tara, about 20 families are still living at the Radisson Blu Portman Hotel, and Khalid Ahmed, 20, is reaching the end of his tether. Surrounded by silver buckets of white orchids, amid the hubbub of tourists and waistcoated porters pushing polished bronze trolleys piled high with suitcases across the expensively carpeted lobby, he describes living long-term in a hotel as a “nightmare”. “It’s not home,” he says. He is uncomfortable walking past the top-hatted doormen after football training. “They don’t say anything but it’s a four-star hotel. People are in their tuxes and they look at you if you come in in your muddy kit.” He is often surprised by visits from cleaning staff. “It’s one knock, then boom, they come in. It’s a beautiful hotel but I’m not on holiday.”

Although he has a food allowance from the council, he is shocked by the hotel prices (a Red Bull outside costs around £1.19; here a can costs £4.15). He no longer eats at the hotel. Every night, the Grenfell families living here gather in the lobby to talk about housing; their patience is running thin.

“Initially people were angry because of what happened. Now they are getting angry again because it’s all taking so long.” But he is hoping that his time in the hotel will end before he starts his mechanical engineering course in October. His aunt, whom he lives with, has seen a flat she likes, and plans to accept it; they might be able to move within weeks. “It would mean a lot not to be waking up in a business environment every morning. I never thought it would take three months.”