You will need a high level of design skill and creative vision. In practice, many set designers have an art-based BTEC HND or degree.
Several universities, colleges offer useful subjects such as interior design, fine art, 3-D design - check with colleges or universities for course entry requirements.
Whatever your qualifications, you should find practical work experience and build a portfolio or 'showreel' DVD of your design work to show to potential employers.
You could get relevant experience through getting involved with activities such as student or community events.