López Ufarte was born in Fes, Morocco. His parents, from Andalusia and Catalonia, moved abroad in search of work, and returned to Irun (Basque Country) when their son was eight. After making his early footballing efforts at neighbouring Real Unión he signed for Real Sociedad, making his La Liga debut in the 1975–76 season, playing his first game in the competition on 30 November 1975 in a 0–2 derby away loss against Athletic Bilbao aged only 17. From then on he became an essential first-team member, scoring 16 goals in 63 matches in the side's back-to-back league titles.