Of these victims, five have been formally identified.
That number may still change, Met Police Commander Stuart Cundy said in a statement.
Some people are believed to have lost more than one family member.
A further 18 people are still in hospital, nine of whom are in critical care.
A one-minute’s silence was held across the UK at 11:00 BST on Monday to remember the victims.
Four confirmed dead named so far
Anthony Disson was confirmed to have died by police on Monday.
The 65-year-old retired lorry driver lived on the 22nd floor of Grenfell Tower.
Mr Disson, who had lived in the property for eight years, phoned his son at 03:30 and said he was being told to stay in his flat.
“Our family are devastated at receiving the news that Tony sadly did not survive the fire,” Mr Disson’s family said in a statement.
“Tony leaves behind a large family, his wife, sons and grandchildren, including one grandchild he will never get to meet.
“We miss him terribly, and are pulling together as a family and trying to stay strong under these tragic circumstances.
“We ask at this time that our family are left to grieve in private.”
Abufars Ibrahim, 39, was confirmed to have died by police on Monday.
Five-year-old Isaac Shawo has been described by his mother as a “beautiful boy”.
He was a pupil at Saint Francis of Assisi Catholic Primary School and lived in Grenfell Tower with parents Genet Shawo and Paulos Petakle, and his three-year-old brother, Luca.
Isaac reportedly became separated from his family in the smoke.
Artist and photographer Khadija Saye, 24, whose work is being shown in the Venice Biennale, lived on the 20th floor with her mother, Mary Mendy, who is missing.
Labour MP David Lammy confirmed her death, writing on Twitter: “May you rest in peace Khadija Saye. God bless your beautiful soul. My heart breaks today. I mourn the tragic loss of a wonderful young woman.”
Khadija’s work in Venice is based on Gambian spiritual practices and is being shown in the Diaspora Pavilion.
She had written on Facebook: “It’s been a real journey, tears shed, highs and lows, but mama, I’m an artist exhibiting at the Venice Biennale and the blessings are abundant!”
Syrian refugee Mohammed Alhajali, 23, came to the UK in 2014 and was studying civil engineering.
His family have described him as a “a very amazing and kind person”.
“He came to the UK because he had ambitions and aims for his life and for his family.
“Our whole family will miss Mohammed dearly and he will never be forgotten.
“To God we belong and to him we return.”, the family said in a statement.
He had been in a 14th floor flat with his brother Omar but the pair lost each other in their attempt to escape.
Mohammed then returned to the flat and tried to call family members in Syria but could not get connected to them, so spoke on the phone to a friend in the country for two hours while he waited to be rescued.
The brothers had been due to join the Syria Solidarity Campaign on Saturday to take part in the Great Get Together, celebrating the life of murdered MP Jo Cox and marking Refugee Week.
Families appeal for the missing
Appeals have been made on social media for news of missing friends and family, and posters have been pinned up around the neighbourhood.
An emergency number – 0800 0961 233 – has been set up for anyone concerned about loved ones.
Six members of the Choucair family lived in a flat on the 20th floor.
Sawsan Choucair fears they are dead. Her mother Sirria, sister Nadia and brother-in-law Bassam are missing, as well as children Zainab, Fatima and Mierna aged three, 10 and 13.
Omar Belkadi, Farah Hamdan and Leena Belkadi
Omar Belkadi and his wife, Farah Hamdan, are unaccounted for, as well as their six-month-old baby, Leena.
The couple lived on the 20th floor. Two of their children, aged eight and 10, were found alive in hospital.
Farah’s cousin Adel Chaoui told the BBC that Farah called her sister while the fire was raging to ask for advice.
“When we told them to get out, Farah said she was told to stay put, not to go anywhere,” he said.
“That was the last we heard. We don’t know whether the authorities got up to the 20th floor to find the children. We’ve had no more information from them,” he said.
Khadija Khalloufi, 52, lived on the 17th floor with her husband, Sabah Abdullah.
Mr Abdullah told the BBC that since the fire the council has moved him from a hotel to an old people’s home despite his objections. He is the only resident from Grenfell Tower living there.
Steven Power, 63, lived on the 15th floor.
A family member confirmed he has not been seen since the fire.
Zainab and Jeremiah Dean
Zainab, 32, and her son Jeremiah, aged two, are missing. It is believed they lived on the 14th floor.
Zainab’s cousin Francis Deen told the BBC the family had no new information.
Francis spoke to Zainab on the phone while she and her son were trapped.
He said the phone had gone dead in the early hours of the morning.
“I am assuming they might never be found,” Francis said.
He has now given DNA samples to police.
Sakineh Afrasehabi and Fatima Afrasiabi
Two sisters from the same family have not been since the fire.
Sakineh Afrasehabi lived on the 18th floor. Her sister Fatima Afrasiabi went to visit her on Tuesday night.
Their family believe they went up to the 23rd floor to escape smoke from the fire.
“My brother was on the phone to our mum while it was happening – we haven’t heard much from the authorities since,” Sakineh’s daughter, Nazanin, told the BBC.
Mary A Mendy
Mary Mendy’s family have confirmed that she is one of the missing. She lived on the 20th floor with her daughter Khadija Saye, who has been confirmed dead.
Brkite and Biruk Haftom
Mother and son Brkite and Biruk Haftom lived in flat 155 of Grenfell Tower.
Family friend Dejan Araya says Brkite’s sister and friend have been searching hospitals for news of their whereabouts and are inconsolable.
Dejan Araya said the last time there was any contact with them was at around 22:00 BST on the night of the fire.
Deborah Lamprell, 45, lives on the 16th floor. A family friend said she would always text her mother when she returned home from work.
The last text message Ms Lamprell sent her mother was at about 23:30 BST on the evening of the fire. She has not been heard from since.
Ms Lamprell’s cousin made an appeal on Facebook for information. She posted: “Dear friends, I am desperate for your help. My cousin Deborah Lamprell lives in Grenfell Tower.
“We haven’t had any news and don’t know if she’s been rescued and in hospital.”
Raymond “Moses” Bernard
Raymond Bernard, known affectionately as Moses to friends, lived on the 23rd floor.
Friends have put up posters of Mr Bernard asking for information about his whereabouts.
“There are a lot of people grieving for him, and he was a very loving man.
“He always used to make sure that people were cared for,” a friend, Michael, said.
Gloria Trevisan and Marco Gottardi
It is believed Mr Gottardi and his girlfriend Ms Trevisan were staying with friends at Grenfell Tower.
Mr Gottardi’s father, Giannino, told Italy’s ANSA news agency that he had been on the phone to his son and his girlfriend up until the last minute.
He told him that the flat was full of smoke and then communications were interrupted.
“We’re just hoping for a miracle,” he said.
Mr Gottardi, an architect, is from a town near Venice and Ms Trevisan is from the city of Padua.
Five members of the El-Wahabi family are missing. Sanaa Jones says they are her uncle Abdul Aziz, 52, his wife Fouzia, 42, son Yasin, 21, daughter Nur Huda, 15, and youngest son Medhi, eight.
Sanaa’s other aunt, her husband, and two children – who also live in the same block – were able to escape from the sixth floor, but the El-Wahabis were on the 21st floor.
“My aunty told my uncle to get out but there was a lot of smoke,” she said
“My uncle got on the phone to the fire brigade, who advised him to stay inside and to shut the door, and put blankets down around 02:30 BST.
“That’s the last time we heard from them.
“I went to one hospital, my cousins went to other hospitals. There is nothing and they are not there.
“It’s very distressing time at the moment. We have to try to keep strong,” she added.
Hesham Rahman, 57, lived alone on the 23rd floor.
His sister, Noha, wrote on Twitter on Friday that she still had no news.
“We are so desperate” she said.
The Philippines Embassy, in London, has appealed for information about 79-year-old Ligaya Moore, who lived on the 21st floor.
Iranian-born Hamid Kani, 61, lived alone in flat 154. A London-based family friend says his relatives in Iran are devastated as they cannot reach him.
They have been trying to get information from hospitals but have not been able to locate him.
The family friend – who wishes to remain anonymous – said it has been a stressful and painful time for the whole family.
Mohamednur ‘Mo’ Tuccu
Mo Tuccu, a British national from Eritrea, was visiting friends or family at Grenfell Tower with his wife Amalahmedin (also known as Samia) and three-year-old daughter Amaya.
They had gone to break their Ramadan fast.
A colleague at the Red PR consultancy – where Mr Tuccu has worked as a security guard for 10 years – said he was due to win an award for his service to the company.
The company tweeted an appeal for news of his whereabouts on Thursday.
Mohamed ‘Saber’ Neda
It is believed that Mohamed Neda’s wife and son fled the blaze but he stayed behind because he was injured.
His nephew says he has been missing since then and the family have left signs around the area to try to get more information.
In a Facebook appeal, family friend Ariana Neumann Rodger said: “We know a family that’s been involved in the fire.
“They are called the Nedas and are the most wonderful family of Afghan Brits who have worked with us for many years.
“The 22-year-old son, Farhad, is being treated at Chelsea and Westminster, the mother Folora ‘Shakila’ is in intensive care at King’s College Hospital and the dad Mohamed ‘Saber’ is missing.
“They lived on the 20th floor and Mohamed Neda was last seen on the stairwell injured and helping neighbours.”
Marjorie and Ernie Vital
Marjorie and Ernie Vital live on the 16th floor of Grenfell Tower.
Marjorie’s brother Macleod says it has been an intense time for the family who are very distressed and concerned.
He said he had been visiting hospitals and centres to try to locate his sister and nephew.
One family from the 17th floor has five people missing. Husna Begum, 22, and four other members of her family were last heard of at 03:00 on Wednesday.
Husna and her mother Rabiya Begum, father Komru Miah, who is aged nearly 90, and two brothers Abdul Hamid 28, and Abdul Hanif 25, are all missing.
Husna’s cousin Abdur Rahim, who lives close by in Kensington, said he got a phone call from her at 01:30 saying there was a fire and they were stuck inside.
He rushed to the tower and spoke to them on the phone asking them to flee.
Husna Begum told him it was all dark, there was a lot of smoke, and they couldn’t get out of their flat.
Mr Rahim said in an interview with the BBC Bangla service that Hasna was due to get married on 29 July and her husband-to-be had rushed down from Leicester after the incident.
Another family member, Mr Nurul Islam, expressed his anger on Friday that he feels the council and government are providing insufficient help and resources on the ground at Grenfell Tower.
“Where are government officials? Where are council officials?” he said.
“There isn’t any leadership or co-ordination – the Red Cross and Muslim Aid are here, but they are charities, they are not people who’ve been elected to support us in times of need.”
Jessica Urbano Ramirez
The family of Jessica, aged 12, say they are desperate for news about her whereabouts.
Her aunt Ana Ospina says they have been calling hospitals as they believe she may have been taken in for treatment.
Actor Noel Clarke, who grew up in the area, is one of many social media users appealing for information on her whereabouts.
Mariem Elgwahry, 27, is a marketing manager who is believed to have last spoken to someone at 02:30.
Her friend posted this picture with the message: “Seeking any information on our missing friend. She was on the 19th floor.”
Ali Yawar Jafari
Ali Yawar Jafari, 82, lived on the 11th floor of Grenfell Tower with his wife and daughter.
His son Hamid says his father had a heart condition and had difficulty walking.
His daughter Nadia was visiting on Tuesday evening, and when the fire broke out she got into the lift with him.
But they separated on the 10th floor, and the family have not been able to contact him since.
Mr Jafari has lived in the tower for 16 years. He is a father of six children and seven grandchildren.
The family of 56-year-old Denis Murphy say they last heard from him in the early hours of Wednesday sometime between 01:30 and 02:00.
He called from his flat on the 14th floor and said he couldn’t breathe because of the smoke.
His family say they have not heard anything since and have been frantically contacting hospitals and care centres.
By BBC’s UGC and Social News team
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