Roger Payne, the BMC's national officer, said the group's Russian guide was responsible, and that it was the second serious incident involving British climbers on the 18,400ft (5,600m) Mount Elbrus, in the Caucasus, in the past year.
The Russian Committee on Emergency Situations which announced the discovery of the four men - John Milledge, 28, a Sheffield doctor; Kenneth White, 42, a civil servant from Dumbarton; Myles Plant, 42, a building inspector from Lincoln; and Thomas Keely, 27, a computer engineer from Manchester - claimed their Russian mountain guide Anatole Yanochkin had led them to safety.
But Mr Payne said: 'Every mountain has a local climate and rapidly changing weather. If the Russians are claiming their guide was responsible for this group's survival then he was also responsible for the predicament they got into in the first place.'
The BMC is concerned that guides in countries like Russia are desperate to promote adventure holidays and are taking unnecessary risks. The council will consider the problem at a conference next month.
The four men found yesterday were with a 15-strong party which split into three to climb the mountain. One group turned back because of the weather, another returned after scaling the peak, and the four men and their guide were reported missing.
Climbers familiar with the mountain believe the group lost its way in a blizzard and took a different descent route from the rest of the party. A rescue team of 20 Russian mountaineers and two helicopters had been hampered in their search by appalling weather conditions.
According to the Committee on Emergency Situations the group arrived yesterday morning in the town of Pyatigorsk, 60 miles from Terskol, their base camp. The British embassy in Moscow said the men were 'in fine shape, and elated that they escaped an awful fate'.
Mr Payne said the BMC had received serious complaints following a series of incidents involving the same holiday company, High Adventure, at Mount Elbrus last year.
'A man who slipped and injured his head on Mount Elbrus was abandoned while the guide led the rest of the group to the top of the mountain. When they had gone, he fell again and suffered further injuries.
'Then, when the group returned, the group were led over an area known to have crevasses. One of the party fell into a crevasse and was seriously injured, but the guide did not have a rope to rescue him. The climbers had to improvise using their rucksack straps.'
He added: 'A guide takes responsibility for a group. There is a clear duty of care. There were at least two potentially fatal accidents. These people were not being properly cared for.'