Researchers believe the results may partially explain why far more climbers die coming down from the Everest than they do going up.
Asked whether the same impact might be seen after surgery, the study leader Professor Stanton Newman, dean of the School of Health Sciences at City, said: "Absolutely. What we found is that there was a clear relationship between levels of hypoxia and brain function which has not been established before.
"It was possible to group people into three groups, some of whom had mild effects, and some whom it was significant. We noticed that it was worse for older people.
"We know that a number of people who go back to work after surgery and find that they have cognitive problems but it was unclear what was causing it.
"We also noticed that the declines happened even when people were given oxygen and their oxygen levels returned to normal."
The team used the climbers to study the effects of hypoxia because it would be unethical to deprive humans of oxygen in trials.
Participants received a series of neuropsychological tests assessing memory, language, attention, and executive function.
These were administered at sea level in London, 3475m at Namche Bazaar in Nepal, and at 5180m at Everest Base Camp.
Tests were also conducted upon return to 1280m in Kathmandu. This group was also compared with a control group.
Hypoxia can also be caused by lung diseases such as emphysema, bronchitis and pneumonia where sufferers struggle to take in enough air. The research was published in the journal PLOS One.