"It is with our deepest regrets that we report the passing of Peter Kinloch, who was a bright spark in our team, and he is missed very much," the statement said.
It did not give details of Kinloch's death. He was climbing the 29,035-foot (8,850-meter) mountain from the Chinese side.
It was not clear whether an attempt would be made to retrieve his body. The bodies of other climbers have been left on the mountain in the past because of the harsh conditions.
"The geography of the area is very complicated, and the weather is often bad. Add the severe lack of oxygen, and it's extremely hard for rescue work to be successfully carried out there," Wang Yongfeng, vice chairman of the China Mountaineering Association, told The Associated Press.
Kinloch is the fourth person to die among people climbing Everest from the Chinese side this year, Wang said. The mountain straddles China and Nepal.
"Mountaineering is a high-risk event, and the mountaineers are all aware of the risk beforehand," Wang said.
A British embassy spokesman in Beijing could not immediately be reached Thursday.
Kinloch's death came three days after a 13-year-old American boy, Jordan Romero, became the youngest person to reach the top of Mount Everest. Romero also climbed the Chinese side of the mountain.