I'm an engineer and have worked in aerospace for over ten years and other sectors for another ten, I don't have an aerospace degree, a few comments:
Most engineering degrees will have at least 50% of the syllabus in common, maths, mechanics, materials etc.
Most (all) aerospace companies take grads and interns from a wide range of specialisms, I work with systems engineers, materials engineers, coders, automation experts, mechanical engineers, electrical, chemists, data analysts, stress etc etc. The vast majority of technical roles are very specialised.
Look at degree apprenticeships, Airbus, RR, BAE, etc. You get a degree, no fees, a salary, guaranteed internships, needless to say competition for places is pretty strong.
For aero look at UWE, Bristol, Bath, imperial, Cranfield, Loughborough, Manchester,
An MEng is pretty much standard and PHD or EngDoc very sought after.
Oh, and enjoy, I love what I do.