Tests examined the safety of cladding in combination with a polyethylene filler and stone insulation.
Of the 111 buildings to fail the test, 90 are local authority or housing association-owned.
Rockwool, the makers of the insulation, said the test does not properly assess their product.
They say it is non-combustible and has the highest grade for fire resistance worldwide.
The Local Government Association said the 16 councils that own the affected blocks were already taking safety steps.
The test is the second of six ordered by the government and takes the total number of buildings that do not comply with current building regulations to 193.
Last week, it was revealed that the combination of materials used on the facades of 82 towers had failed the first of the six cladding combinations being looked at.
Cladding samples from all 111 blocks had already failed the initial combustibility tests, also conducted by the Building Research Establishment (BRE).
Initial safety testing after the fire, which killed at least 80 people, only tested the combustibility of the cladding.
However, the new tests involve a 9m demonstration wall subjected to a replication of "a severe fire in a flat breaking out of a window" to see if the flames then spread up the exterior.
The six new tests were rolled out at the recommendation of an independent expert.
The second series of government safety tests - the first of a wave of more comprehensive assessments - has now been completed, the Department for Communities and Local Government (DCLG) said.
It said cladding systems using aluminium composite material (ACM) panels with a polyethylene filler, and stone wool insulation "does not meet current building regulation guidance".
It is suspected that ACM panels on the outside of Grenfell Tower fuelled the spread of the fatal blaze, acting as kindling once the fire took hold.
Cllr Simon Blackburn, from the Local Government Association, said councils "will continue to get on with what they need to do to ensure people are safe in their homes".
"This includes replacing materials on high-rise blocks affected by these fire safety tests," he said.
"The government must commit to meet the full cost to councils of removing and replacing cladding and insulation systems.
"It is also imperative that this testing process moves quickly to identify what landlords should be replacing these systems with as soon as possible."
It comes as the Grenfell Response Team said most survivors of the fire were still living in emergency accommodation.
Residents from 13 homes have been rehoused so far, with 48 out of 175 offers of temporary or permanent accommodation being accepted.
More than 100 buildings have failed the latest fire safety tests set up in the wake of the Grenfell Tower fire, the government has said.