. "If a student is doing history then [schools] are advising them to take geography as well, and the same with sciences and languages.
"That then uses up the option categories, so you have all the other subjects competing for just one slot. The Department for Education says Progress 8 is designed to protect a broad and balanced curriculum, but because of the EBac being used as an accountability measure, schools are gaming it."
The issue has prompted a "marked" increase in phone calls and emails from DATA members, Mr Green added.
The National Society for Education in Art and Design also said it was aware of creative subjects being hit. "Our own research showed that 44 per cent of schools believed the new measure would have a negative impact on creative subjects," said general secretary Lesley Butterworth.
Peter Nutkins, headteacher of Humphrey Perkins School in Loughborough and a member of the Heads for the Arts pressure group, said schools were attempting to play the system.
"If you make a set of qualifications the `gold standard' alongside others that don't have the same value, that builds inequality into the system," he added. "Heads are under huge pressure to deliver on outcomes, with their jobs placed at risk, so they will try to maximise those outcomes at the expense of a broad and balanced curriculum."
Last week Ed Miliband pledged that, under a Labour government, schools would be judged "outstanding" by Ofsted only if they offered creative subjects. And last month he told TES that the "denigration" of creativity under the coalition was "really terrible".
The Warwick Commission's report reveals that the number of GCSE students taking design and technology dropped by half between 2003 and 2013. Entries to drama and craft-related subjects also fell, by 23 per cent and 25 per cent respectively.
Mary Boyle, principal of Knole Academy in Kent, an expressive arts school, said it took a great deal of "bravery" for headteachers to continue to offer a broad curriculum.
A DfE spokeswoman said there was "no evidence" to back up the subject associations' claims. "Schools should always put the interests of their pupils first and offer rigorous, high-quality courses that give them the skills and experience they need to succeed in modern Britain," she added.