Clearly for your first job it will have some importance. If you have Oxford written all over your CV that will open a few extra doors, as they have a reputation and quality that is well know within the aviation world.
However later in your career it will have little importance, as long as you gain some experience. But it does help - I would rather buy a Mercedes then a Honda, even though I know the Honda is good, the reputation of Mercedes preceeds the brand!