Mrs May was greeted with cries of "coward" and "shame on you" as she returned to the site of the devastating fire in west London on Friday.
Thirty people are now known to have died in the blaze, six of whom have been provisionally identified.
London Police said an investigation had been launched to determine whether the blaze involved any crimes and May announced a public inquiry, a type of probe that's used to investigate issues of major public concern.
Earlier today, Scotland Yard expressed fears that all the victims of the massive fire that engulfed a 24-storey tower in west London may never be identified.
Prime Minister Theresa May has faced heavy criticism for failing to meet survivors of the deadly Grenfell Tower blaze during a "private visit" to the scene of the devastation on Thursday afternoon.
He also said survivors from the tower would be re-housed in the local area.
"Government is making money available, we are ensuring we are going to get to the bottom of what happened, we will ensure that people are rehoused, but we need to make sure that that actually happens".
Ade Deane-Pratt from Camberwell, south London said she was marching because of the anger she felt towards the Government.
Yesterday, Queen Elizabeth and the Duke of Cambridge met volunteers, residents and community representatives while visiting Westway Sports Centre, near the charred remains of the tower block in north Kensington.
London police arrest another suspect in connection with London Bridge attack
Canadian Prime Minister Justin Trudeau condemned the attack and said on Sunday he was "heartbroken" that a Canadian was among those killed.
Cundy said one of the victims was a person who died in hospital.
Around 800 people gathered outside Prime Minister Theresa May's residence at Downing Street to protest against the United Kingdom government's handling of the disaster, said Joey Ayoub, a journalist and activist who joined others at Number 10.
"This is an absolutely very bad fire that took place".
More than 3 million pounds ($3.8 million) has been raised for victims of the London high-rise fire that has killed at least 30 people and left dozens homeless.
The emergency fire arrangements given to residents during the refurbishment of their tower advised them to stay in their flats, because flat fire doors gave emergency crews 30 minutes to rescue them.
There has been growing fury on the low-rent estate where residents wanted answers on why the fire was able to spread so rapidly and why complaints about safety had been ignored.
Grief and disbelief at seeing a tower that had been home to up to 600 people reduced to a burned-out shell turned to outrage and anger.
It said the company that manufactured the cladding also made fire-resistant models that cost fractionally more than the standard version.
As of Friday morning, authorities have not determined the cause of the fire. One Moroccan woman in the mosque, Habiba, said she was looking for a 16-year-old Moroccan school girl Nur Huda El Wahabi who is missing, who is best friends with her son Abdul.
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