Most consultancies with an International Development focus will require five to ten years experience, although there are graduate training programmes for specialist Development organisations and more general Professional Services consultancies that have an involvement with the Developing world.
While academic backgrounds in economics and accountancy will have a clear application in the consultancy arena there are opportunities for those with other qualifications.
In the book 'Getting into International Development'
For more information and resources on consultancy careers see the Private Companies and Consultants Sector pages.