We consider the most general class of supersymmetric solutions of D = 11 supergravity consisting of a warped product of AdS₅ with a six-dimensional internal manifold N₆, which are dual to N = 2 super conformal field theories in d = 4. For any such N₆ we construct the full non-linear Kaluza-Klein ansatz for the reduction of D = 11 supergravity on N₆ down to D = 5 SU(2) × U(1) gauged supergravity, at the level of the bosonic fields. This allows one to uplift any solution of the D = 5 supergravity to obtain a solution of D = 11 supergravity for any given N₆. Using an explicit N₆, corresponding to M5-branes wrapping holomorphic curves in a Calabi-Yau two-fold, we uplift some solutions and comment upon their interpretation.