Some fascinating footage there. I remember the European Cups of the 70s and 80s when English teams dominated the competition and did well in the UEFA Cup and the European Cup Winners Cup.
It's worth observing that back then you only played 3 knockout rounds to reach the final, so to win it you only played 7 games as opposed to the 13 which it now takes to win the CL. Also, because only the league champions entered, you could win it without ever meeting a big club. If you look at who Liverpool, Forest and Villa actually played in the seasons when they won the EC, you'll find they were playing teams in the quarters and semis who never even get near the group stage these days.
That's not to belittle what they achieved, but it's surprising that Forest were able to win it 2 years running without ever meeting Real Madrid, Barcelona, AC Milan, Inter, Juventus, Bayern Munich. Mind you, it's still possible for us to reach the final without playing any of them either.