Can't choose between a Math&Philosophy and Design Engineering degree

I just finished my As levels in maths, further maths and physics.

As I really loved and enjoyed my core maths modules and I had some experiences in philosophy (talkes by academics) I decided to look up for degrees in maths and philosophy. The idea to study these two subjects is really thrilling me because I consider them the two most pure sources of knowledge. I like using abstract contents and investigate them in a completely logical way.

But I also find interesting the new technologies developed by companies like google and sony, so I searched for some courses related to this and I found out Design Engineering offered by Imperial, Bristol and a couple of other unis. Reading the structure of this course really excited me as it's exactly the type of engineering that I was looking for. It offers you a wide range of modules (mechanics, computing, robotics, electronics) and all of this is combined with design and gives you everything you need to design, develop, produce and sell your own product.

Now I need to decide between the two as Im gonna apply for unis next year and Im completely lost at the moment.

I will really appreciate any suggestion and advice from you guy, especially those who have done/are doing this sort of degrees.

Thanks