The Women’s Equality party is to launch an unprecedented campaign aimed at radically changing the way the fashion industry treats body size and shape.

Coinciding with London fashion week, which will run from 16-20 September, the initiative will call for an end to unrealistically small “sample sizes” – the sizes in which designers show their new creations – and demand a minimum body mass index (BMI) for models.

Sophie Walker, the WEP leader, plans to ask the London mayor, Sadiq Khan, to withdraw funding for next year’s fashion week if the campaign’s key demands are not in place by then. She will also ask Maria Miller, chair of the Women and Equalities Commission, to hold a public hearing in which fashion designers will be asked why their clothes are based on “an unattainable level of thinness in women”, which Walker believes is contributing to a crisis in public health with an economic impact of £1.3bn a year.

The campaign calls for models whose BMI is below 18.5 to be seen by a medical professional from an accredited list, who will judge whether they are well enough to be employed by a modelling agency. Similar legislation exists in France, Spain, Italy and Israel. Campaigners are also asking that fashion designers showing at LFW commit to including at least two sample sizes in every range, one of which must be a UK size 12 or above.

Additional proposals include fashion magazines committing to at least one piece in each issue featuring plus-size models. WEP is also demanding that body image awareness become a compulsory part of personal, social and health education, with a focus on media depictions of beauty and extra training for teachers.

Those backing the campaign include Caryn Franklin, the former presenter of The Clothes Show, who is now a professor of diversity in fashion at Kingston University, plus-size model Jada Sezer and model Rosie Nixon, who has spoken out against an industry that asked her to lose an unreasonable and unhealthy amount of weight in order that she get “down to the bone”.

WEP will also launch an interactive social media campaign, #NoSizeFitsAll, based on the statistic that one in five women cut the labels out of their clothes to conceal their size. A photoshoot will feature new designers Isatu Harrison and her line, Izelia, and Katie Pope of Pope London, both of whose work will be modelled by a diverse group of women.

Walker describes the initiative as a chance to “raise awareness of the body image issues experienced by women and girls, and to have a discussion about the significant and far-reaching impact of the fashion industry’s idolisation of a unique and very small size”.