A Briton and an American were among at least 21 people killed in the militant attack on a hotel and office complex in Nairobi on Tuesday, officials and relatives have said.

The Briton was named by his employer, the charity Gatsby Africa, as Luke Potter, its Africa programmes director. In a statement, it said he had devoted the past 10 years to helping some of the poorest and most vulnerable people in the world.

“Luke was respected by all he worked with, bringing huge drive, determination, a relentless work ethic, and a thirst for new ideas to every project,” the statement said. “He brought a calm head and his unique sense of humour to every situation … He was our colleague and our friend.”

The charity said it shared the grief of his family, partner, daughter and friends. Nic Hailey, the British high commissioner in Nairobi, said authorities were providing support to his family and friends.

Facebook Twitter Pinterest Luke Potter, who died during the attack in Nairobi. Photograph: Gatsby Africa

Another British person was wounded and was receiving medical attention, the Foreign Office said.

Jason Spindler, the American who died, was the director of a business development firm who was based in the Kenyan capital, and had survived the September 11 attacks in New York.

“It’s with a heavy heart that I announce that my brother, Jason Spindler, passed away this morning during a terror attack in Nairobi,” his brother Jonathan wrote on Facebook. “Jason was a survivor of 9/11 and a fighter. I am sure he gave them hell.”

Eleven Kenyans were confirmed dead, a mortuary official told Agence France-Presse. One victim had no papers, the official added.

The London-based consultancy firm Adam Smith International said two of its employees had died on the terrace of a restaurant in the complex, where the company has offices. Abdalla Dahir and Feisal Ahmed, Kenyans of Somali descent, had been working on the Somalia Stability Fund managed by ASI to “bring peace and prosperity to Somalia”, the company said. Fifty staff and consultants were safely evacuated, it added.

Another victim was named as James Oduor, commonly known as Cobra.

Oduor, known for his love of football, was tweeting as the attack was going on, asking people outside the complex what was going on. “What’s happening at 14 Riverside man? We’re trapped in our buildings.” he said in one message. He worked for an electrical company in the building.

Kenya’s president, Uhuru Kenyatta, said early on Wednesday that security forces had ended operations at the dusitD2 hotel, having killed all four attackers.

A member of the British SAS took part in the mission to end the assault, photos from the scene showed. The heavily armed man with a military vest and balaclava worked with local forces and helping victims leave the complex. It was reported the lone SAS member took part in the operation alongside US Navy seals, having been in the country to train Kenyan special forces. The MoD said it did not comment on special forces.

Facebook Twitter Pinterest An SAS member helps escort an injured man from the scene of Tuesday’s attack. Photograph: Dai Kurokawa/EPA

Families who went to the Chiromo morgue were told they could not view the bodies until a forensic investigation had been performed, provoking grief and anger.

The family of a missing 35-year-old man collapsed in the courtyard upon hearing that a body had arrived with his identification papers. “He is gone, he is gone,” the father repeated into his phone as his mother wrapped a shawl around herself and wept.

A woman who gave her name as Njoki wept as she said: “My sister is not in any of the hospitals and the last time we spoke she was a bit calm but suddenly she started crying and shouting and I could hear gunshots and her phone remained on but she wasn’t speaking. We have no doubt her body is here. Let them allow us in.”

As other families pleaded to be allowed access, an elderly couple arrived in silence, bringing a freshly pressed suit to dress their dead son.

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Hiram Macharia, a marketing executive at LG Electronics, said he and some colleagues had been rescued by police from their office two hours after the attack began, but that one workmate did not survive.

“One of our colleagues went to the top of the building and his body was found there,” Macharia said outside the hotel.

Kenyatta said more than 700 civilians were safely evacuated from the complex.

The assault began shortly after 3pm on Tuesday with an explosion in the parking lot and then a suicide bomb blast in the hotel’s foyer. It was claimed by al-Shabaab, the militant Islamist organisation based in neighbouring Somalia that carried out the 2013 attack on Nairobi’s Westgate mall that left at least 67 dead.

A woman rescued from the hair salon she manages in the dusitD2 complex on Tuesday also survived the Westgate attack, local media reported. “I was working there when the attackers stormed in, it was not easy just like today. All I can say is that I thank God,” Tracy Wanjiru told Nairobi News.

Wanjiru said she heard a loud explosion on Tuesday and went out to see what was happening. “I jumped back to the salon, told my colleagues we were under attack. They dismissed me at first but when they heard wails and screams, everyone went into hiding,” she said.