Liverpool were drawn against Sparta Prague in the last 16 of the Europa League, while Brighton face another tough test in their first season in Europe, with a tie against Roma.
West Ham will face their pool-stage opponents Freiburg again, while Rangers will take on Benfica.
All four British teams have the advantage of playing their second legs at home, courtesy of topping their groups.
They will travel to play their first legs on March 7, with the second legs to be played a week later on March 14.
Liverpool will be pleased to have avoided the more dangerous-looking sides, especially Bundesliga leaders Bayer Leverkusen, who face a long trip to Azerbaijan to play Qarabag, and AC Milan, who face Slavia Prague.
Jurgen Klopp will also be pleased to have sidestepped Roma, who Brighton will take on in the next chapter of their memorable maiden European journey.
West Ham will be confident, having done the double over Freiburg in the group stages, winning 2-1 in Germany and 2-0 in London.
Rangers, high on confidence as they top the Scottish Premiership, will fancy their chances of bloddying the nose of another European big gun in Benfica.
Aston Villa will discover their last-16 opponents in the Europa Conference League when the draw for that competition takes place at midday on Friday.
