Former US Army doctor, Dr Craig Stark, helped treat casualties following the incident.
Dr Stark, who now works for a company which has hospitals across the continent, was in Nairobi for work. He told Forces News: "One of our hospitals is in Nairobi and happened to be in the vicinity of the attack.
"When we heard what was going on, my team and I showed up at the hospital and we knew we'd be receiving casualties, so we set our mass casualty plan into effect and mobilised the doctors, nurses and technicians and waited for the first casualties to come in.
"My experience is as a US Army doctor and a flight surgeon, so I have a lot of experience in disaster response, international health.
"Even though it's been many years since I left, the training that you get in the military immediately comes back to you and when that mass casualty occurs, your training kicks in and you know what to do."
The Kenya Red Cross said it was helping families searching for loved ones missing since the attack began.
The British Army Training Unit in Kenya (BATUK) has a permanent base in Nanyuki, around 120 miles from Nairobi, with a smaller element in the country's capital.
The unit consists of around 100 permanent staff and a short tour cohort of 280 personnel, according to the MOD.
Under an agreement with the Kenyan government, up to six infantry battalions per year carry out eight-week exercises in the country, along with Royal Engineer exercises and medical deployments.