I personally think Motorsport degrees kind of push you in to a corner a little, however as noted as long as they're giving you a good amount of general mechanical engineering course.
I'd say find a good uni with a Mechanical Engineering degree and a half decent Formula Student team then you're set for both worlds. Gives you 3 or 4 years of motorsport experience and applies your skills well.
There's plenty of companies that wont even look at engineering grads that havn't done Formula Student, or at least they'll almost certainly be looked at.
Being IMechE accredited is what you need, and ideally you want to do an MEng course if you want to become chartered.
Thank you for this info, very interesting. I hadn't even considered formula student. A lot to consider all in all.
Thanks to everyone who has replied so far.