The son of a man who fell to his death from the top floor of Grenfell Tower has accused the fire brigade of giving “false hope” and ultimately costing lives by telling residents that rescuers were on their way.

Farhad Neda, 25, who managed to escape with his mother, Flora, from the 23rd floor, told the public inquiry into the disaster that residents were “fatally let down” because the firefighters never came.

His mother told the inquiry the firefighters’ advice to residents to stay put destroyed the lives not only of those who died but many more people.

“Those people who died on the night of fire, the only cause of their death is the stay put policy,” Flora Neda said. “If they didn’t believe the fire brigade … I am sure they would be alive, including my husband. The fire brigade has to take responsibility for their mistakes.”

Flora’s husband, Mohamed Saber Neda, 57, a former Afghan army officer who fled the Taliban in 1998 and who worked as a chauffeur in London, died with four neighbours who had taken refuge in their flat, number 205.

Farhad Neda said his father was a hero because he stayed to help Mariem Elgwahry and her mother, Elsah, and Sakina Afrasahabi and her sister, Fatima , rather than try to escape. They had come up from the floors below to escape the rising flames and smoke. They all died.

Farhad, a former British taekwondo international, told Richard Millett QC, the counsel for the inquiry, that he took hold of his disabled mother and started descending the stairs in thick black smoke. They had expected his father and the others to follow.

His father’s body was found outside the tower with injuries consistent with falling from height. Flora Neda said he had jumped.

“He could have come with us,” Farhad said. “However, he did not leave those women who were distressed and needed help in our flat. He died trying to save their lives.”

He said that one of the Afrasahabi sisters had been told a helicopter might rescue them if they went to the top floor, but conditions in the flat were so bad shortly before they fled that Flora was ready to jump rather than go through the pain of being burnt alive.

The inquiry saw WhatsApp messages between Farhad and a friend who was not in the building. She sent him a picture of the tower ablaze at about 2am. He told her: “The fire is reaching us. Our noses are full of black smoke. We are getting worried. Is there any hope?” She replied: “Please keep calm. Hopefully everything will be ok.”

Facebook Twitter Pinterest The WhatsApp messages between Farhad Neda and a friend who was not in the building. Photograph: Grenfell Tower Inquiry

Farhad described the “nightmare” of his descent with his mother on his back. “We were stepping and tripping over dead bodies as people had already died in the stairwell,” he said. “I can still hear the sounds of people desperately struggling to breathe. It sounded like they were snoring, as they choked for their last remaining gasps of air.” When his mother asked what the obstructions were, he said they were fire hoses because he didn’t want to upset her.

They were met by firefighters part of the way down the tower and were escorted out. Farhad told the inquiry that the firefighters, although brave, “did not really know what to do”. They did not seem to have enough oxygen to work higher up in the tower or to share with residents coming down.”

In a separate statement, Ahmed Elgwahry, Mariem’s brother, described how he stayed on the phone to his sister as she and his mother died in flat 205. He said he urged them to escape by the stairs, but his sister said she wasn’t able to because of the smoke. He suspected it was because his mother’s mobility was poor and his sister didn’t want to leave her.

Eventually she could no longer speak and made a deep humming noise instead. He asked her to bang the floor if she was still there, and she did. He heard his mother saying in Arabic “I can’t breathe” and then there was silence. He stayed on the line long after they had died.

“I could hear the fire entering the flat from the window,” he said. “I will never forget how violent and aggressive it sounded. I could hear it penetrating through the flat and heard bubbling noises. I could hear pots and pans falling and smashing everywhere.”

Farhad said he had long been concerned about fire safety, especially since the building’s refurbishment in 2016, which included the installation of combustible cladding. The closing mechanism on their fire door had broken soon after the refurbishment and the landlord had not fixed it.

He was also worried that new gas pipes might fuel a fire and that large holes drilled between floors to fit new pipes might cause problems.

Flora said that as well as numerous problems with the refurbishment, residents repeatedly complained to the landlord about there being only a single staircase in the event of a fire. “They didn’t listen to us,” she said.

Farhad told the inquiry he was struggling to cope with the disaster. “Losing my dad, my home, and losing my friends in the Grenfell Tower fire has left me feeling very lost,” he said.

“I do not think I have had the chance to grieve for him properly … I have not yet dealt with the events that unfolded on 14 June 2017.”