Consta began his professional career as mechanical engineer, specialising in hydraulics and energy. Alter three years in the field of appropriate energies (National award of engineer in Colombia, 1979), he began to work with indigenous and campesino communities in Colombia and with NGOs in Latin America. 

In 1988 he went to work for Oxfam Novib, where he worked with development projects in Honduras, Guatemala and El Salvador. In the 1990s, Consta worked with El Taller's education programme in Tunis, directed the Citizens Diplomacy Programme in Mexico.

Since 1999 he has been working with Oxfam GB, first as Oxfam GB Country Director for Colombia and now as Policy Adviser in the Economic Justice team based in Oxford.  He is also a member of the Oxfam International Land Grabs team.