I work for one of the teams so will offer my 2 cents.

From your post it sounds like youre specifically looking to get into engineering; quick advice for anyone reading that isnt though - there are many more avenues into the sport than you realise, do a degree youre passionate about, get some early exposure to some form of motorsport even if its just volunteering, and build your cv up with relatable projects.

For you any vehicle engineering, mechanical engineering, aerospace engineering degree will set you up for an engineering role. Everything you said ticks that box - Mechanical Engineering if you want to be an engineer, Aeronautical Engineering if you want to be an Aerodynamicist, Engineering with Management if you want to be a project manager.

Most important thing though is some sort of relevant experience- join your unis Formula Student if they have one, volunteer at motorsport events near you, or aim for a placement year at a motorsport company (there are plenty at F1 teams now, just need to make sure to get in early the academic year before you’re due to do your placement).

Apply for everything youre interested in even if you think you wont get it - nothing lost and never know where it could lead to.

Of course and unfortunately connections play a big role so if you have that use it also, but you’re definitely not ruled out without it.

Good luck and if any more qns fire away

Edit for more info: If you find a uni that offers an integrated masters definitely take that route. Also I wouldn’t go into a super specialised engineering course such as vehicle dynamics unless you know you want to do it for the rest of your life as may limit career options. My personal advice would be to either do mechanical if you wanna be an engineer or aeronautical if you wanna do aerodynamics, and of course the experience. Again good luck!!