The idea had been recommended by the British Fashion Council after last year's size zero debate but it's already been ruled out in New York, Paris and Milan, BBC Radio reports.
London Fashion Week kicked off Sunday.
Officials in the three cities said forcing models to produce a medical certificate was too invasive.
Eating disorder charities have criticised the decision.
The size zero debate began when two South American models died from eating disorders.
In response, the British Fashion Council came out with 14 proposals last September in a report called the Model Health Inquiry.
One of the main proposals was to introduce health certificates for models on Britain's catwalks.
Catwalk models make up only 10 per cent of the modelling population.
But officials in New York, Paris and Milan did not agree with the proposals.
They said the measures were unworkable and discriminated against other models who didn't appear on the catwalk.
Karen Diamond, the director of Models One, the largest modelling agency in Europe, said: "The idea of a model health certificate is not a bad idea in itself, but it's just impossible to police and to govern.
"That's why it hasn't been implemented at this stage because there's just no way of doing it.
"Who's to say that a girl who gets this certificate, lets say it's valid for a year, isn't going to be OK in six months time or a year's time. You just don't know.
"The girls generally are not unhealthy."
But eating disorder charities are unhappy with the decision to drop the health certificate proposal. They say fashion bosses are guilty of a U-turn and young models could become victims of conditions like anorexia.
Susan Ringwood from BEAT (Beating Eating Disorders) said models should be championing a healthy body image.
"The British Fashion Council have stepped away from one of the fundamental recommendations of the Model Health Inquiry," she said.
"Fashion is fantastic, it can be wonderful but there are some aspects of it that are still actually quite toxic."
Some of the inquiry's recommendations have already been put in to practice though.
They include banning under-16s from London Fashion Week catwalks and making sure that the shows have healthy backstage environments for models.