The toll had previously been put at 30.
She has promised those left homeless would be rehoused locally within weeks, and the £5m fund would pay for emergency supplies, food, clothes and other costs.
May said phone lines at the Council would be better staffed and more staff would be deployed in the area. "What we are doing is putting in place the support that will help them", she added.
The statement officially confirmed that a 23-year-old Syrian refugee was the first victim of the huge fire.
The identification of the victims is proving very hard - which experts attribute to the extreme heat of the fire.
May is chairing a government task force on the fire and a spokesman says that she will meet afterward with "a group of residents, victims, volunteers and community leaders" at No. 10 Downing Street.
"There is considerable damage within Grenfell Tower", he said.
Sabres Expansion Draft Protected List
Commissioner Gary Bettman suggested recently that the upper limit might remain at or close to last year's mark of $73 million. When it came to protected players, much of the Blackhawks' situation was easy to figure out due to their contract situations.
"We entirely support the calling of the public inquiry and will co-operate in whatever way we can with it so that local people have all the answers about what has happened", the council said.
The identification of the victims is proving very hard - which experts attribute to the extreme heat of the fire. London Police's investigation remains on-going, as fire crews continue the grim and slow task of identifying and recovering bodies from inside the tower.
Police say the harrowing search for remains had been paused Friday because of safety concerns at the blacked tower but has resumed.
The fire broke out at the 24-storey block, which contained 120 one and two-bedroom flats, in the early hours of Wednesday morning.
Some of the anger stems from reports that Grenfell Tower had no central sprinkler system and was built with flammable materials that residents told the government needed to be fixed.
"The fire at Grenfell Tower was an unimaginable tragedy for the community, and for our country".
"Little can compare in recent times to a tragedy on this scale - the response from the local authority has simply not been good enough". More than three million pounds ($3.8m) have been raised for the affected families. British press is reporting that as many as 70 people are still missing and unaccounted for in the tower.
Numerous displaced are living in churches and community centers.
"My understanding is that the cladding that was reported wasn't in accordance with United Kingdom building regulations", Hands told Sky News. "We were seeking a change to the building regulations for that very objective", he added.
Another, larger protest also marched through west London, where hundreds of people headed to the burned-out building tower. "We've always been advocates of automatic fire sprinkler protection in tall tower blocks and they work - people don't die in sprinkler buildings", he said.