My 'support' for English teams in European games depends entirely on who is playing. I absolutely hate with a passion the scum and the blue scum, so I always want them to lose every game they play, except when the play each other in which case I hope that the scum lose. Therefore, in European games I would always cheer on the foreign opposition, no matter who they were.
I have always like Man Utd, they play great football and have had lots of players over the years who I have greatly admired, so I will usually cheer them on. It used to be the same for Liverpool, but over the last few years I've come to really dislike them so I doubt I'd cheer them on, but wouldn't necessarily care either way. I don't like Stoke so couldn't give a toss about them winning or losing in Europe, but I did get behind Fulham when they had that great run in Europe a couple of years ago, because I liked them as a team and they were very entertaining.
I don't hate Emirates Marketing Project enough (yet) to really be wanting them to lose in Europe, so to an extent I don't really care so long as they don't end up winning the Europa league, which would just make their fans even more intolerably smug.