Most Grenfell Tower survivors are still living in hotels three weeks after the deadly blaze as the Government attempts to find them suitable accommodation.
Fourteen households hoping to be moved out of emergency accommodation have accepted offers for more permanent living arrangements, Grenfell Response Team (GRT) said.
Campaigners and residents claim little headway has been made, with residents said to have been offered properties that are either out of the borough, too expensive or on a one-year contract.
It also emerged that a specialist taskforce will be sent in to Kensington and Chelsea Council to take over the running of key services, following heavy criticism of its response to the disaster.
Some 139 offers had been made following 158 housing needs assessments by Wednesday - the three-week deadline the Government set itself for offering housing to all of those displaced by the blaze.
GRT said every household that wanted to move from emergency accommodation had been made offers in Kensington and Chelsea or neighbouring boroughs, while 19 families were contacted and had either refused assistance or were abroad.
This was for a range of reasons, including some relatives who were looking after loved ones in hospital, and the response team was "ready to provide them with accommodation when they were ready".
One resident reported being shown a two-bedroom property when they required three bedrooms, others had been offered places in high-rises, and another survivor was said to have been offered accommodation with the caveat that no guests could stay overnight.
GRT has said rent will be suspended for one year and thereafter will be of a "similar scale to a council house social rent", while survivors should feel under no pressure to take up the first offers.
Grenfell survivor Sid-Ali Atmani, currently living in a hotel, turned down the offer of a home because it was too far from the area and the local school.
He told the BBC Radio 4 Today programme: "Some families ... they don't want a temporary house. Personally, I speak with a few families, they are not asking for a temporary house.
"Can the Government give them back their houses, their life back? We are not the criminals here, the crime has been happening in the building."
Pilgrim Tucker, a campaigner working with Grenfell Tower families, told the Press Association: "Their concern is they are not being talked to properly, just being presented with an offer.
"People are being texted saying 'Here is your offer, it is rent-free for a year and then it is £400 a week' - that is triple what they are paying before."
She said the example of tripled rent had come from one specific survivor from the tower. It is not clear how many others had been offered similar deals.
Jamal Williams, a resident from a nearby block which has also been evacuated, said he had spoken to a woman who had been offered a place in Harlesden.
He expressed concerns over the clarity of tenancy agreements, adding: "The concern is what it will be afterwards. I think people are looking for a lifetime tenancy arrangement."
A spokesman for the North Kensington Law Centre said many of its clients were still staying in short-term, temporary accommodation such as hotels and B&Bs.
It said there were "unanswered questions about whether those residents will have to pay more rent than they did previously, and whether their new tenancies, both temporary and permanent, will guarantee them the same rights and protections they had before".
Most of the 160 households evacuated from the "finger blocks" surrounding the tower - Testerton Walk, Hurstway Walk and Barandon Walk - are still in emergency accommodation, a Kensington and Chelsea Council spokesman said.
A number of households had gone back to their homes, he said, while some families were returning in the day to cook meals and spending the nights in hotels.
Repair work on a broken boiler affecting the properties was due to be completed by Wednesday, he added.
It was also revealed that cladding from 190 high-rise buildings in 51 local authority areas have failed combustibility tests conducted by the Department for Communities and Local Government (DCLG).
Every sample sent in has been found to be combustible, continuing the 100% failure rate, the DCLG said.
Buildings at three NHS trusts in England - North Middlesex University Hospitals, King's College Hospital and Sheffield Children's NHS Trusts - have also failed the tests, health officials said.
Cabinet minister Chris Grayling would not put a deadline on finding permanent accommodation for the Grenfell survivors.
"It's going to depend on the individual families. They are taking decisions about their own circumstances and we want to work with them to make sure those decisions are the right ones for them," he told the Today programme.
The Transport Secretary added: "No local authority in London simply has a big block of vacant permanent accommodation available, so what we are trying to do is make sure that people are properly housed in the meantime and those permanent solutions are available as quickly as possible.
"All of us feel desperately, desperately sorry and concerned for those who have been through such a traumatic event and everyone wants to get their lives back to normal as quickly as possible."