Experts believe the exterior cladding, which contained insulation, helped spread the flames quickly along the outside of the tower in the June 14 blaze.
Commander Stuart Cundy of the Metropolitan Police said that 16 bodies had been recovered from the 24-storey building in west London, but stressed that although investigators had reached the top of the tower the hard search could take weeks or longer because of the level of damage to the structure.
"I would like to reassure everybody that we will be looking at all criminal offenses that may have been committed by any individual or any organization", said Cundy.
However, five people who were originally reported as missing have since been found safe and well.
"Sadly, for many families, they have lost more than one family member, and my heart truly goes out to them", he said.
The fire triggered both sorrow and outrage, as residents described the futility of their earlier attempts to have the building's safety issues addressed, particularly its fire escape plan.
In addition to the questions surrounding the building's cladding - fitted to the high rise as part of a refurbishment project - the tower, built in the 1970s, also didn't have a sprinkler system installed.
Meanwhile, in Australia, authorities are calling for a nation-wide crackdown of the use of similar cladding.
The venue had been a focal point for efforts to support those affected by the fire which engulfed the apartment tower in a matter of minutes.
At least 58 people are dead or presumed dead and many others are homeless.
Cundy said police had now managed to get to the top of the tower and had undertaken a first visual search for victims, ahead of later painstaking searches.
Faith leaders also called for "immediate action" to provide counselling and support services to ensure health and wellbeing to all those who are suffering, particularly the children.