Alan Brooke-Dean, from Dorset, died in Verbier on Monday. Mr Brooke-Dean, who would have been 50 today, was with seven others.
He was crushed when a 1,500ft section of an off-piste snowpack slid on to his group. Survivors raised the alarm and four helicopters, seven dogs and a 60-strong team were sent.
Yesterday Swiss officials said they were likely to bill Mr Brooke-Dean's estate for the cost of the operation, because preliminary investigation showed he had contributed to the avalanche by ignoring signs alerting skiers to the dangers of off-piste conditions.
Pascal Fournier, of Air Glaciers, which mounted the rescue, said: "In Switzerland it is the person who is rescued or their insurance company that normally pays for the rescue operation. This operation could cost 50,000 Swiss francs (pounds 22,000) ... it may have been their [the group's] fault that the avalanche started." But Mr Fournier added that it was difficult to tell exactly how avalanches start.
A Briton who died in an avalanche in Val-d'Isere, France, on Tuesday was a chalet manager, Mark Wilson.