No, essentially. There are no courses in aerodynamics, propulsion, mechanics of aircraft, aerothermodynamics, or aerospace control systems modules at Exeter (unless they've introduced them since I was there, which I don't think they have). They do cover some overlapping topics like thermofluids and mechanics of materials, but this won't be particularly applied to aerospace purposes.
You would probably need to aim for a masters in aerospace after such a degree to move into that area. However it is fairly common to do a BEng in mechanical/materials/electronic (or sometimes civil) engineering, then a masters in aerospace engineering to go into the field, since at least historically aerospace engineering wasn't that common as an undergrad course (it's moderately common these days).
If you know you want to go into that field though, you may as well do the more specialised course now. Also I would note Exeter's engineering department is fairly mediocre and nothing at all compared to Loughborough's which is in a whole other league to Exeter tbh. I can't say after my time doing engineering at Exeter I'd recommend it over a department like Loughborough.