Survivors and relatives of victims from Grenfell Tower have said they feel “vindicated” by the inquiry’s initial report into the fire that killed 72 people nearly two-and-a-half years ago.

At an emotional press conference following publication of Sir Martin Moore-Bick’s interim report, bereaved family members stood in silence for 72 seconds – one for each of those killed by the 14 June 2017 blaze.

A group of eight relatives and survivors from the upper floors welcomed official criticism of the failure of the London fire brigade (LFB) to carry out more effective rescues and reluctance to evacuate the burning building.

The relatives also questioned the testimony of firefighters and asked why their loved ones had been told to stay put while others were helped down the stairs. The decision of some firefighters not to give statements to the inquiry was deplored.

Shah Aghlani – whose mother, Sakina Afrasehabi, and aunt, Fatima Afrasehabi – died on the 18th floor of the tower, said the inquiry had found the LFB was “unprofessional and inadequately trained”. The service needed a “total overhaul”, he added, and Dany Cotton, the London fire commissioner, should consider her position.

Nazanin Aghlani, the daughter of Sakina Afrasehabi, agreed: “However brave the firefighters were, there was a serious lack of common sense. They didn’t see, especially at senior levels, what was so vivid in front of them.

“We look at firefighters as heroes ... but they are not heroes, they are professionals. It’s quite evident that the whole LFB ... is in the hands of people that are incapable of their jobs. They should be prosecuted [for corporate manslaughter]. I’m not saying individual firemen, they do a hard job ... but the seniors at the top get good money to do a very serious job.”

Paulos Tekle, whose five-year-old son Isaac perished in a smoke-logged stairwell, wanted to know why “we were told to stay [in their 13th floor flat] while other families were told to leave”.

Tekle said: “My friend advised us to go but we trusted the authorities. We believed the firefighters who told us to stay.” When they were eventually brought down, his son was being held by the hand but his grip slipped and he disappeared in the smoke. “How come they did not see the little boy? We were hoping to be rescued.”

Flora Neda had lived on the 23rd floor of Grenfell with her son, Farhad, and husband, Saber, for 20 years. When other families, fleeing the flames climbed up to their floor she believed they had been misled by firefighters suggesting they could be rescued by helicopter.

“I knew there was no way you could get out on to the roof,” she said. After about 45 minutes, when thicker smoke began to appear, her son carried her down the stairs. “We used the staircase from the top down to the ground floor.” She had thought she would see firefighters earlier but did not meet them until the 4th floor.

Her husband, a former Afghan army officer, stayed behind to help two neighbours who were too scared to leave. He left it too late to escape and, as the flames closed in, jumped from the 23rd floor to his death.

Neda and her son were the only two survivors from Grenfell’s highest floor. “I believe [my husband] would be alive, along with the other 21 people up there, if they had not listened to firefighters telling them to stay put.”

Nabil Choucair, who lost six members of his family on the top floors of Grenfell, criticised the LFB for passing on blame to the cladding on the building. “They should have implemented a rescue mission much earlier. Has Dany Cotton not learnt anything from what happened that night?”

Hamdan El-Alami sobbed uncontrollably as he told the press conference how he had lost his daughter, son-in-law and two grandchildren in the fire.

Elsewhere in west London, Zoë Dainton, 32, who lived in Grenfell Tower for 25 years, said the report exceeded her expectations. “The inquiry has listened to us. Everything I said in my statement to the first phase, he has listened to. Now they need to keep on listening.”

Tiago Alves, 22, was among the survivors pleased by the judgment that the cladding broke building regulations, partly because it means the issue will not have to be debated in the second phase of the inquiry examining the role of the council, builders, architects and cladding and insulation manufacturers.

“Because this is illegal, the rest of the country shouldn’t have this on their buildings,” he said. “We are going to get to a point where life will get safer for people living in other buildings.”