The idea was recommended by an inquiry last year into the health of fashion models.
Hilary Riva, chief executive of the British Fashion Council, wrote in an open letter: "Industry representatives advise us that any unilateral action by London Fashion Week will mean that models will decline to work in London which is already the least commercially attractive of the four major fashion weeks.
"Without internationally recognised catwalk models our designers will not want to show here."
London Fashion Week, which begins on Sunday, is vulnerable to a boycott because more than 70 per cent of the models who appear are based overseas.
The BFC insists it is committed to introducing the certificates. Some of the inquiry's recommendations have been implemented, including banning under 16s from the catwalks at London Fashion Week.
