I did Mat Sci at Loughborough and worked with Williams F1 and Lotus indirectly (I got to consult on materials failures with them, but couldn't say I worked for them directly)
- from what I saw they are only really interested in the most exceptional talent. So yes a decent Uni is expected but it has to be more than that. My mate won young Engineer of the Year and was exceptional on our course, he went to JLR. The best in my year went to work in cutting edge military design - so I know F1 might sound exciting and glamorous but there are other exciting fields you may yet not know about yet
If I was set on trying to do something like that today I would go to lots of Uni Open Days and see what connections the academic staff have to the right places, have they had placements students or graduates go there?
Knowing the right people can make a big difference in opening the right doors. LinkedIn might help you find some helpful stuff too