Mohammad Niazi and Musa Popal were killed after a blast shook the Afghan capital on Thursday.
Zohra Popal said her father was said to be waving his British passport at US troops when the explosion occurred.
Mr Popal, 60, and Mr Niazi, died as thousands waited for evacuation outside Kabul airport after the Taliban seized control of the city.
The UK Foreign Office has so far confirmed two British nationals and the child of a British national were killed in the attack.
Mr Popal ran the Madeena Supermarket in Hendon, north London, for more than 20 years and had travelled to Afghanistan in June with his wife to visit family.
His daughter Zohra said her mother survived the blast, but Mr Popal's 14-year-old grandson Hameed was still missing.
Zohra, who moved to the UK to join her parents in 2014, said: "My mother, she had to crawl away, covered in blood and pieces of people. She saw everything.
"There was blood everywhere, she told us, and they were slipping in it when they were trying to get up.
"It was so loud that some of them are still deaf and can't hear each other. It was a living nightmare for them.
"Had we known anything like this would happen, we wouldn't have let them go."
She said her mother had lost everything in the bombing, including her documents, and that she and other relatives were still in danger after the UK's withdrawal on Saturday.
Describing her father as "loving" and "supportive", Ms Popal said he had always helped her with her assignments at the College of North West London.
Ms Popal said she had yet to be contacted by the Foreign Office following her father's death.
Mohammad Niazi - a taxi driver living in Farnborough - was also killed in the attack after he travelled to Afghanistan to help his family get inside the airport.
Friends believe his Afghan wife and children - who were thought to be having visa problems - were also killed.
One of his friends, Dinez Carnay, said Mr Niazi had told him he was flying to Afghanistan to get his family and that was the last he had heard.He told the BBC: "When you know somebody and suddenly you learn he passed away, especially in a very difficult circumstance, then all you have to do is to pray for the soul."
Mr Niazi's brother Abdul Hamid said he was killed during the firing in the aftermath of the blast.
As many as 170 people died in the suicide attack, including 13 US service personnel.