Design Engineering? Where to study?

Can someone advise me on where to study for Design Engineering/Product Design Engineering? I've got Imperial and Glasgow down but I'm looking at Bath and Bristol but they have the same entry requirements as Imperial so I'm scared I might not get in/an offer.

I'm a Scottish student btw and I've got 4A's (including maths and physics) and 1B in my Highers. I'm taking 3 Advanced Highers (Maths, Mathematics of Mechanics and Physics). I'm looking for a good uni btw.

Thanks!