Hello Sam,
I'm currently in my second year at the University of Hertfordshire studying a BSc in Motorsport Technology trying to get on a 12month placement scheme within the formula 1 and motorsport teams around the globe, so i'll be able to pass on some useful info.
There are many universities out there that hold degrees in aerospace & mechnical engineering and a little more specialised ones such as Motorsport technology or engineering.
The engineering course that would best for you is simply the one you have the most interest in from the courses mentioned in the previous paragraph and are surprisingly similar just with some different modules which you can specifically look for on any university website.
In an aerospace engineering/technology degree (i know friends that are en-rolled on) you will cover mathematics in engineering, computer aided design; were you can actually design parts and actual vehicles, thermofluid experimental engineering; more physics based, modern technologies within aerospace which you can learn and even work with. All in all it doesn't matter what engineering degree you take, you will take similar if not the same modules at some point at university.
From here you can apply for 12 month placements schemes in your 3rd, 4th year depending on the course to F1 and general motorsport teams which the lecturers can give you advice and even directly getting in contact with people who are currently working in the motorsport sector.
I doesn't really matter what company you work for such Airbus, BAE systems etc. just make sure you're one day qualified to take on a certain role in a motorsport team.
Overall it isn't easy but as long as you stick in with your studies and work hard there's always opportunities and getting to know people within the profession is very important.
Hope this helped.