A team of civil servants has been embedded in the Council office after residents complained they had been left with little support or information from officials, the BBC reported.
At least 58 people are dead or presumed dead and many others are homeless. Thirty of the victims are confirmed dead. The death toll is expected to rise.
The Council says it will cooperate "in full" with the government's inquiry.
The recovery operation in the 24-storey tower has resumed but could take weeks, the BBC said.
Council leader Nicholas Paget-Brown says questions about how the fatal fire spread so quickly through the tower block "will be answered".
Meanwhile, the Home Office said it was making arrangements for the family of one of those who died in the fire to travel from Syria to Britain for his funeral.
Mohammed Alhajali, who was 23 and a civil engineering student, was the first victim to be named.
Following criticisms of the Kensington and Chelsea Council's handling of the disaster, Paget-Brown said "lessons must be learned". He said he was "heartbroken by the tragic fire and the appalling loss of life".
On Saturday, British Prime Minister Theresa May admitted support for families "who needed help or basic information in the initial hours after this appalling disaster was not good enough".
The statement came after May met volunteers and some of the people made homeless by the fire. One of them told reporters they spoken to the Prime Minister for two and a half hours about their demands and what they expected.
Residents caught up in the fire have previously condemned the relief effort as "absolute chaos".
May said phone lines at the Council would be better staffed and more staff would be deployed in the area.
They would wear high-visibility clothing so that they could easily be found, dispense advice and ensure the right support was provided, she added.
May said she expected to announce the name of the judge for a public inquiry within a few days. The inquiry will report back to the Prime Minister.
She has told Councils to complete urgent safety checks on similar tower blocks.
May has come in for a barrage of criticism over her response to the disaster, including being jeered when she visited the North Kensington estate on Friday.
On Saturday afternoon, hundreds of protesters gathered in Whitehall to call for her resignation.
The government has committed 5 million pounds for clothes, food and emergency supplies for the victims.
The fire broke out at the 24-storey block, which contained 120 one- and two-bedroom flats, shortly before 1 a.m. on Wednesday.
It tore through all floors of the building and took more than 200 firefighters and 24 hours to bring it under control.
Two neighbouring Tube lines are to be partly suspended into a second day amid safety concerns of debris falling on to the tracks.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
About VDC
Doraiah Chowdary Vundavally is a Software engineer at VTech . He is the news editor of SocialNews.XYZ and Freelance writer-contributes Telugu and English Columns on Films, Politics, and Gossips. He is the primary contributor for South Cinema Section of SocialNews.XYZ. His mission is to help to develop SocialNews.XYZ into a News website that has no bias or judgement towards any.