The measure is one of a raft of recommendations proposed by a British model health inquiry panel last year.
The British Fashion Council yesterday said its counterparts in New York, Milan and Paris are not supportive of an international medical health certification scheme.
The British Fashion Council may seek government advice on brokering an internationally recognised agreement if resistance continues, it said.
Models based overseas may refuse to participate in London Fashion Week if it is the only such event requiring them to have health checks, according to the council which owns and organises the bi-annual event.
A lack of high-profile catwalk models would in turn discourage designers from showing their collections in London.
More than 70% of London Fashion Week models are based overseas, with many arriving just hours before the shows start.
In an open letter regarding the model health inquiry, council chief executive Hilary Rivas said her counterparts in Milan, New York and Paris are unenthusiastic about medical certificates for models.
“Model industry representatives advise us that any unilateral action by London Fashion Week will simply mean that models will decline to work in London, which is already the least commercially attractive of the four major fashion weeks,” she said.