Well, it depends on how much less prestigious I guess. Maybe not against a 1st from other good but not top-5 unis, but I think it could do against a 2.1, or a 1st from TVU! Warwick seems to be much better regarded than I thought it was while I was there...
To be honest, I'm not one of those people who believe that a 1st is a 1st and it doesn't matter where you went to uni, otherwise there'll be no point in going through the whole admission process, interviews etc. etc. I think it does matter, in some cases it can give you the edge, but that I doubt an Oxford tutor who, at interview, faces an extremely bright and passionate student with good or great academic record, will deny him admission just because he went to XY university.