He was the son of Francisco Benjumea y Heredia (1908-1995), 3rd Count of Guadalhorce, and his wife Matilde Cabeza de Vaca y Garret (1915-2006), XVI Marquise of Valdecañas, Marquise of Torremayor, XVI Countess of Peñón de la Vega.
He received his doctorate in the Higher Technical School of Mining Engineers (Polytechnic University of Madrid).
Subsequently, by means of a Fulbright scholarship completed a master's degree in Civil Engineering at the University of Michigan.
The couple had six children: Blanca, Rafael, José, Tilda, Enrique and Isabel.
Since then and until his death, Benjumea assumed the presidency of his board of trustees, and promoted Spanish-US relations in various scientific disciplines (architecture, medicine, economy, conservation of the heritage, among others).