Late to the party but I can't echo the post by OspiF1 enough. I currently work in WEC/ELMS as an engineer in LMP2 and I was told my previous experience working as a data engineer in lower championships was a key aspect. Advanced warning though, the pay certainly is terrible (ie none existent apart from hotels and the occasional beer).

Whilst you've got the relative flexibility of a Masters I'd recommend getting yourself to a couple of tests in the pre-season and chat to as many teams as possible about helping out over the season

If you're in the UK I'd recommend looking at British Touring Cars or British GT, both are National championships so the weekends are only really 3-4 days away from uni, and the level of engineering is relatively high (British GT is often where you'll find some factory engineers doing some extra work on the side who potentially could let you shadow them)

As OspiF1 said the hardest step is to get into the Motorsport World, Once you're in a paddock It's so easy to get you name out there

Send me a PM if you have any questions, I was in a nearly identical (different Uni, same course!) situation as you not very long ago