After finally leaving Ferrari at the end of 1976, Regazzoni joined the Ensign and Shadow teams, before moving to Williams in 1979, where he took the British team's first ever Grand Prix victory, the 1979 British Grand Prix at Silverstone.
Finalmente, logo de deixar Ferrari a finais de 1976, Regazzoni uniuse aos equipos Ensign e Shadow, antes de trasladarse a Williams en 1979, onde obtivo a primeira vitoria nun Gran Premio para o equipo británico, o Gran Premio do Reino Unido de 1979 en Silverstone.