Nottingham Forest. Forest won the English League in 1978 before winning the European Cup in 1979 and defending it in 1980. They did not win the English League in 1979.
Forest are the only club to have won the European Cup more times (twice) than they have won their domestic league (once). Manchester United, in 1999, were the first team to have won the tournament having won neither their domestic league nor the European Cup / Champions League the previous season. Liverpool's 2019 triumph came 29 years after their previous domestic league title.