The Government wants to make modern languages and design and technology optional at key stage 4 to free up curriculum time.
The move has been criticised as an underhand means of solving teacher shortages in these subjects. It has also prompted a wider debate about what pupils need to equip them for the modern world.
The Nuffield language inquiry team, led by Sir Trevor McDonald, warned that removing languages from the core curriculum would seriously damage national competitiveness.
It also warned it would be "disastrous for university language departments and teacher supply".
Steven Fawkes, a past president of the Association for Language Learning, which has 5,500 members, said: "How can the Government possibly overlook the huge gap ... in language skills, at a time when global communication is at a premium?"
The Design and Technology Association warned that cuts would endanger Britain's status as a world leader in the subject.
Andy Breckon, the association's chief executive, said: "Germany, Australia and the Far East all admire the new technology that has been introduced here and the impact of high-quality designing skills on young people's thinking. "The sad part is that decision-makers continue to show social prejudices against learning through doing and learning to do."
Professor David Hargreaves, former head of the Qualifications and Curriculum Authority, said two years ago that design and technology should be at the centre of the curriculum. But commenting on the Green Paper last week, he said that squabbling about which subjects should or should not be compulsory was a "distraction".
Consultation on the Green Paper 14-19: Extending Opportunities, Raising Standards closes on May 31