As above, design engineering courses tend to be less mathematical. Imperial's design engineering course is a spinout of it's fairly successful innovation design engineering masters that is co-taught with the Royal College of Art. They also accepted non-engineering grads for that, and didn't require very intensive mathematical background. Thus, unless you're artistically inclined, you may find it disappointing.
Of the courses indicated, Aerospace would probably be the most mathematical, followed closely by Mechanical. You may want to reconsider your other options if you want to apply to very mathematical courses - while those two courses at Imperial, and the Cambridge course naturally, will both be quite mathematically advanced, the others are less likely to be (particularly in the design engineering bracket). You may want to consider applying to an Engineering Mathematics/joint honours in Maths and Engineering course for some of your other ones (such as Bristol's very good course).