Piles of prams, luggage, food supplies, toys and furniture could be seen stacked on the streets as mourners and well-wishers wrote messages of solidarity and hope on posters near the ruined tower.
Commander Stuart Cundy of the Metropolitan Police said: "This is going to be a long and complex recovery operation and I do anticipate that the number of fatalities will sadly increase beyond those 12".
Many of those evacuated said the fire had spread incredibly quickly with nearly no warning and multiple residents told CNN they did not hear fire alarms when the blaze broke out. Thirty-seven people remained in hospital, with 17 of them in critical care. Entire families were missing, and the death toll is certain to rise.
More than £1 million has been raised to help those affected as fire tore through the 24-storey building while volunteers and charities helped with feed and shelter people who could not return to their homes overnight.
After visiting emergency teams at the scene of the blaze in west London, Mrs May said a proper public investigation was needed to establish what happened.
He also called for an investigation into reports that Gavin Barwell, the former housing minister who was recently appointed as the Prime Minister's adviser, had failed to OK a fire safety review request he had received.More news: Search for victims at London high-rise fire continues
More news: No UK govt deal likely Wednesday due to London fire: DUP
More news: Will Trump Try to Block Comey's Testimony?
Some Queenslanders are living in "ticking time bombs" and are at risk of a deadly fire, similar to the London tragedy, the state's peak building and construction group Master Builders Queensland (MBQ) has said.
The Queen has paid tribute to the "bravery" of firefighters who have battled the Grenfell Tower fire. "It is also heartening to see the incredible generosity of community volunteers rallying to help those affected by this awful event", the queen said. Not only have we installed these sprinklers in each individual home, but they are also in bin storage areas. Many of them have donated water, food and clothing to the nearby St Clement church, where locals have taken refuge.
Adele, who was born in Tottenham, joined the vigil later in the evening. In this case, however, the fire seemed to climb the exterior of the tower so quickly that it overwhelmed protective systems like fire doors.
Harrowing accounts emerged of people trapped inside as the blaze destroyed everything around them, shouting for help and trying to escape through windows using makeshift ropes made from bedsheets. Security cordons were in place around the base of the tower and the ground was littered with charred debris.
Early reports from witnesses at the London fire indicated that there were no sprinklers and that alarms may not have sounded. Fire safety is a top priority for us, and I wanted to reassure our own tower block residents about their safety here in Oxford.
It added: "There have been few recorded incidents of serious fire spread involving external cladding, and, although in our view any loss of life in incidents such as these should be prevented if at all possible, neither have there been many deaths".