In May 1973 he and a number of Madrid-based individuals founded the Grupo Tácito, a group of intellectuals, politicians and journalists, some of them coming from the Franco regime and others from the democratic and monarchist opposition to the dictatorship.

They - by the prospect of Franco's death - advocated a democratic solution to the dictatorial regime and had influence in different sectors linked to the system, and where active during the period of the Spanish Transition between 1973 and 1976.

July 1976 Oreja set out to reform Spain's 1953 Concordat with the Vatican, which resulted the same month in agreements with the Holy See laying out the separation of church and state.

[2] Two months later Oreja signed the Universal Declaration of Human Rights on behalf of Spain.

He continued to be active in many fields, being appointed Head of the Institute for European Studies at the CEU San Pablo University Foundation, Vice-Chair of the BBV Foundation (1996) and Doctor Honoris Causa at Zaragoza and Seville Universities (1996).