Speaking on Monday on BBC Newsnight, Lammy said: “What people say is that if you put the numbers out early, there could be civil unrest. That’s what they say.
When asked by Emily Maitlis: “Do you think that’s right?”, Lammy replied: “I’ve no idea, you’d have to ask the police chief, you’d have to ask Cressida Dick.”
But he conceded: “I am sympathetic to it, I am going to walk alongside those people.
“I wasn’t there, but people on the ground say they saw more than is being suggested.”
Lammy added: “The truth is the media cycle is now beginning to move on to other things, that’s the truth.
“And so what people say is that in two, three weeks’ time, if you start to reveal the numbers, things have moved on.”
Following the interview, Lammy took to Twitter to make clear that he “never said that there is a cover-up” but he has listened to survivors and the community, adding: “I hear their concerns.”
Lammy has spoken numerous times about how the official death toll of 79 does not tally with what survivors have told him.
“The community are not asking for an exact figure but it should be possible for the Government to come up with an estimation of how many people lived in Grenfell,” he tweeted.
He added: “Lack of information is feeding suspicion of a cover-up and driving a wedge between community and Government.”
Since the fire, flammable cladding has been found on 75 tower blocks across 26 local authority areas, leading to urgently send samples for testing.
Last week Lammy gave an emotional speech in the House of Commons where he claimed “rich and powerful organisations get away with crimes” and called on Theresa May to reveal more about an ongoing criminal investigation into the fire.
The community are not asking for an exact figure but it should be possible for the Govnt to come up with an estimation
On Sunday Lammy said: “Residents saw dozens of people jumping out of windows to escape the fire. Bodies piled up in stairwells and corridors. Survivors cannot believe that the death toll has not risen.
“Speaking to people on the ground, there is a huge suspicion of a cover-up, with information being withheld for political reasons in an attempt to avoid fuelling anger or unrest.”
Efforts to identify the dead are slow-moving due to the intensity of the blaze and access to the building over safety fears.
Grenfell fire victims
Logan Gomes, stillborn.
Baby Logan Gomes, who was stillborn in hospital on 14 June, has been recorded by police as a victim of the fire. Pictured are his parents Marcio and Andreia Gomes and their two daughters Megan 10 and Luana, 12.
Majorie Vital, 68
A statement released on behalf of the family of Majorie Vital said: "Majorie was sixty-eight years old and she had worked in the textile industry for many years. She was a beautiful, joyful, independent, intelligent, kind hearted, sensitive individual who dedicated her life to her children. She carried herself with dignity and extended her warmth to family and friends.
"Through her creativity and joy of life she was an inspiration to many of us. She has been prematurely and dramatically taken from this world and will be sadly missed by family and friends, both here in the UK and abroad."
Ali Jafari, 82
A statement released on behalf of the family of Ali Jafari said: “Mr Ali Jafari, aged 82, died following being caught up in the fire at Grenfell Tower. Mr Jafari is survived by his wife, children and grandchildren. Ali was loved and will be greatly missed by his family and the wider community.”
Yahya Hashim, 13
Yahya's mother Noora Jamal, husband Hashim Kidir and children Noora, along with her husband Hashim Kidir and their children Firdaws Kidir, 11 and Yaqub Kidir, 6, remain missing.
Speaking on behalf of his family, his aunt, said:“Yahya: My most kind, handsome, pure hearted, sweet nephew.“You were the most kind, polite, loving, generous, thankful and pure hearted boy I ever knew."
Hamid Kani, 61
His family said: "Hamid will always be remembered for his wit, compassion and devotion to his family and friends.
"No words can express our sorrow for his loss and the way he left us. He will always be part of our lives and his memory will live on."
Zainab Dean, 22
Zainab's father Zainu and mother Maria Deen said: "It is with great sadness that we can confirm we have been notified by the police that our daughter Zainab Deen died in the tragic Grenfell Tower fire.
"Zainab has been missing with her son, our grandchild, Jeremiah, who we still await news on. We respectfully ask to be allowed to grieve privately at this time."Funeral arrangements will now be made and all further updates will come from Zainab's immediate family only."
Marco Gottardi, 27
Pictured here with his girlfriend Gloria Trevisan, who also died in the blaze. The couple, who were both architects, lived on the 23rd floor the 24-storey block.
Gloria Trevisan, 26
The body of the architect was discovered on the 23rd floor, where she lived with her boyfriend Marco Gottardi, Westminster Coroner's Court heard. The young woman is understood to have called her mother in Italy as the fire spread.
Berkti Haftom, 29
Her family said: "Berkti was a generous, caring, loving mother, partner, sister, aunty and friend and she will be missed by us all forever."
Sheila's family, who have asked that her surname is not released to the public, said:"Sheila was a resident of Grenfell Tower for 34 years who absolutely adored her family and gave her many friends much love and inspiration.
"A very active and well-respected member of the local community, Sheila was cycling around London, performing yoga daily and swimming regularly in the Kensington Leisure Centre until she was 80 years old.
"With her exploration of the alternative, in her lifetime she amassed a wealth of knowledge, wrote poetry and philosophical and political thoughts, and created some highly original artwork - nearly all of which now sadly lost in the fire at Grenfell Tower.
"Sheila leaves two sons, six grandchildren and three great-grandchildren. As a family we are heartbroken as to this senseless tragedy that took her far too early, and will do all we can to honour her name."
Rabia Begum and Husna Begum, 22
The bodies of mother and daughter were found in the remains of the Grenfell Tower. Male relatives from the same family Kamru Miah, 82, Hamid, 29 and Hanif, 26 all remain missing.
Farah Hamden, 23, Leena Belkadi, 6 months
The six-month-old baby girl was found in her mother’s arms in a stairwell between the 19th and 20th floors of the tower block, Westminster Coroner’s Court was told. Her father, Omar Belkadi, also died in the blaze.
Omar and Farah's two other daughters were recovered from the 20th floor, where they lived and taken to St Mary’s Hospital. Malek, aged 8, later died. Tazmin, aged 6 remains in hospital.
The 52-year-old has been confirmed as having lost her life along with her daughter Khadija Saye in the blaze at Grenfell.
Her sister Betty Jackson said in a statement on behalf of the family:"My beloved sister, words can never describe the pain of losing you. I can't believe you are gone. You were a wonderful sister, an incredible aunt, the best mother any child could have wished for. You were an amazing friend to all those who knew you.
"Your heart was pure, your soul was one of a kind. You will be missed for a life time. You will remain forever in our hearts. you and your beautiful daughter Khadija Saye.
"From your sister, brothers, nieces and nephews.”
Anthony (Tony) Disson
In a statement, his family said: "Our family are devastated at receiving the news that Tony sadly did not survive the fire at Grenfell Tower.
"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."
The 23-year-old came to Britain from his war-torn home in Daraa, Syria, three years ago. He was separated from his brother Omar, 25, as they tried to flee the fire. Omar is understood to be recovering in hospital.
Ya-Haddy Sisi Saye, also known as Khadija Saye
The 24-year-old was understood to be on the 20th floor with her mother Mary Mendy, 53, when the blaze broke out. It is not yet known if Mendy was able to reach safety.
Family friend and Labour MP David Lammy tweeted his grief on Friday morning, calling her death a “tragic loss” and stating his heart was breaking.
His wife Nicola Green, a portrait artist who had been mentoring Saye told the Evening Standard she last heard from her at 3am on Wednesday when she was Facebook messaging because her phone would not work. She said: “She was saying she just can’t get out and ‘Please pray for me. There’s a fire in my council block. I can’t leave the flat. Please pray for me and my mum.”
Kritchanut via Getty Images
Abufars Ibrahim, 39, died in the fire, the Met Police have confirmed.
Khadija Khalloufi, 52, was the fifth victim named. She lived with her husband Sabah Abdullah on the 17th floor. They both fled their flat but became separated. He told Sky News: 'I opened the door and black smoke came towards our faces, so I grabbed her hand and told her to do like me - pull part of the dressing gown over her nose to filter the air. 'At the 16th floor I looked behind me, she's there... We reached the 15th floor, I look back and I didn't see her.'
The 77-year-old has been identified in agreement with Coroner Dr Fiona Wilcox.
The 44-year-old was identified by dental records and died of breathing in fire fumes, Westminster Coroner's Court heard. He was visiting relatives with his wife Amalahmedin and three-year-old daughter when the fire broke out. They are believed to be still missing.
The five-year-old choked to death on fumes from the fire after becoming separated from his mother, who had wrapped a wet towel around his head. He was found in the lobby of the 13th floor, an inquest at Westminster Coroner's Court heard.
Further people have been identified
PA Wire/PA Images
They have not been named at the request of their families.