Survivors of the Grenfell Tower disaster have said the commissioner of the London fire brigade (LFB), Dany Cotton, is not fit for office, claiming that her response to “dreadful failings” that have emerged since the fire claimed 72 lives “defies belief”.

In closing submissions at the end of the first phase of the public inquiry, counsel for the bereaved, survivors and residents (BSRs) said the fire brigade needed a “shake-up from the top down”. Their demand comes in the wake of mounting evidence about the brigade’s unreadiness for major fires, including radio systems that do not work properly and a lack of training in high rise cladding fires.

They called on the inquiry chairman, Sir Martin Moore-Bick, to deliver “a fearless reckoning” when he publishes his stage-one report next year by also holding to account the Royal Borough of Kensington and Chelsea, which owned the building, as well as the contractor Rydon and the manufacturers of the cladding materials which spread the fire.

Cotton enraged survivors when she gave evidence in September saying she would do nothing differently with the benefit of hindsight. She said she would not train firefighters for a cladding fire any more than she would train them for the space shuttle landing on the Shard.

Danny Friedman QC said this was “insulting” and Sam Stein QC said it left the capital vulnerable to fresh disaster. “Without making sure that the LFB has the resilience and resources to cope with a major disaster, multiple [999] calls and high population risk, then we await the next disaster which will lead to casualties and death,” Stein said.

He likened Cotton’s position to the army saying we’re pretty good at dealing with a minor skirmish but … we’ve given no thought to fighting a battle”.

The lawyers urged Moore-Bick to conclude that the LFB had breached its policies and legal duties in failing to plan or train for the foreseeable event of a fire like Grenfell and that the tower block was in clear breach of building regulations – regardless of calls from the LFB and other parties involved in its refurbishment to await further evidence in the second phase of the inquiry.

Moore-Bick must resist “obfuscation” by companies involved in the refurbishment, said Friedman. “People are here today because they want justice,” he said. “They look to your first report as the beginning of that endeavour.”

Another lawyer, Stephanie Barwise QC, blamed the combustible cladding panels made by Arconic for deaths. She said a decorative crown of cladding at the top of the building had been made from Arconic panels and that its “contribution to lateral fire spread was … devastating, taking 24 lives from the 23rd floor alone”.

She complained of “appalling workmanship” in the building and “abject failure of the design”, telling Moore-Bick: “The inquiry should not be deterred from making findings of non-compliance on the basis of exhortations from Rydon [the main contractor], Arconic and Celotex [an insulation manufacturer] … These corporates simply wish, despite the 72 deaths, to keep kicking the can down the road.”

But it was the leadership of the LFB that was the focus of most of the closing statements on Monday.

Stephen Walsh QC, counsel for the LFB, insisted its firefighters should never have been put in a position where they were trying to save lives in a building that was so combustible. Walsh said firefighters “did not give up because they are hard-wired to save lives while there is still a chance”.

But he admitted: “It is a stark fact that one of the largest fire services in the world was severely challenged, in some elements overwhelmed in the performance of its functions.”

Friedman told the inquiry that shortcomings in the way 999 calls were handled had “undeniably contributed to people dying” and cited “callers being offered the choice whether to stay or go when there was none … being unable to say in the plainest possible terms that pleas for helicopters and high ladders were never going to be met … and failing to carry out callbacks to inform residents who had been told to stay put that they now just had to get out.”

He said fire brigade commanders had failed to respond to what they could see happening in front of them as the fire jumped from flat to flat. They did not account for information about smoke and flames penetrating homes that was coming via phone calls from those trapped in the building, he said.

“They were blind to the obvious need for systematic evacuation,” he said. “This was a devastating episode of looking without seeing and hearing without listening.”

Summing up the situation on the 22nd and 23rd floors, he said: “Reports of fire at 1.30am. No response before 2.08am. And thereafter no systematic approach. The fire on those two floors alone claimed the lives of 36 people, half the number of all the deceased.”

The brigade “should have pursued immediate full evacuation on the night once it was clear that compartmentation of the building had so comprehensively failed. Loudhailers could have been used in the stairwell. The intercom system could have at least been used to wake some people up.”

Friedman accused the Royal Borough of Kensington and Chelsea of breaching the Civil Contingencies Act by not doing enough to provide evidence about residents, building plans and known deficiencies in the fire prevention measures at the building. He said it was necessary to consider the implications of the fact that 90% of those who died were black and minority ethnic people and why so many people with disabilities – which meant they could not be evacuated – had come to be housed on upper floors.

Final statements to part one of the Grenfell inquiry are scheduled to continue on Tuesday and Wednesday. The first stage report is due to be published early next year before the second stage of the inquiry begins.