You might still be escorted to the game by the police as an extra safety measure. Not sure whether that happened previous times English clubs visited. As I said, you should probably ask Spurs/Arsenal/Liverpool/Manchester United/Glasgow Rangers fans about their experience with Belgrade, as they can tell you first hand what's it like for a Brittish person. As far as I know, they didn't have any significant problems, but not sure about police escort.
But it definitely isn't anywhere near as dangerous as I've seen some fans suggest, and unless you purposly provoke them (there are some idiots still who like to pick up fights), you really shouldn't have any problems.