Many residents of the building remain unaccounted for, and police said numerous remains may never be identified.
The latest figure included the previously released number of 30 deaths in the catastrophe in North Kensington early Wednesday.
London has a chronic housing shortage even in the best of times, and those left homeless by the fire - already angry over what they see as government inequity and incompetence - fear being forced out of the British capital.
Cundy added that the police will investigate the refurbishment of the building in 2016 and also vowed to act against those confirmed responsible for the tragedy.
Cundy promised an "exhaustive investigation" into the tragedy and said "my heart goes out to those affected".
Attention has focused on a recent renovation project involving cladding installation as people search for answers on the fire that claimed at least 30 lives.
"I would like to ask anyone who was in Grenfell Tower that night, but for whatever reason has not told us they are safe to please call our Casualty Bureau".
Queen Elizabeth II visited West London to meet with those who were affected by the fire, as did Labour Party leader Jeremy Corbyn.
Britain's high-rise tower blocks dating from the 1960s and 1970s could be torn down after the deadly fire that engulfed the 24-storey Grenfell Tower, London Mayor Sadiq Khan says.
Sinn Fein to meet Theresa May over DUP deal concerns
During the complex talks, the two sides will also have to negotiate a new customs and trade regime between the single market and the UK.
Prime minister Theresa May's government earlier sought to quell anger over the disaster, pledging to support the victims after protesters jeered her when she visited residents. More than 3 million pounds ($3.8 million) have been raised for the victims. "What are you going to do about it?"
As the video continues to record, Rania is heard praying and saying police are telling people to get out but that they can't due to the fire and the smoke.
May met police and firefighters at the West London site on Thursday, to receive a briefing from the emergency services.
He added: "I have said it before, you have my absolute assurance that as soon as I can possibly tell you something that I know to be accurate, I will tell you".
Meanwhile, residents and families met with the Prime Minister at No.10 as Theresa May was blasted for her handling of the disaster.
Emergency workers have reached the top of the 24-story tower, the AP reported.
The fire, which started just before 1:00am on Wednesday, surprised many as they slept and the speed with which it spread shocked fire experts.
Rania is among a number of Egyptians who have gone missing since the Grenfell Tower fire.
Comments