This list provides a reasonable starting point:
It'll take you a long time to work through it all, so I would focus on generally applicable regs (852/2004, 178/2002, 1169/2011 etc) plus more specific ones if/where relevant for the industry sectors you're in (or want to be in).
In parallel to this I'd also be looking at any and all associated guidance - just google for e.g. "852/2004 guidance" etc and you'll find plenty of reading to keep you busy!
Campden runs a two day "introduction to food law" course that appears to attempt to cover almost everything except labelling. Strikes me as an enormous amount of information to try to usefully cover in such a short space of time, but if you specifically wanted a more structured basic introduction and probably a certificate of some sort then they are at least a very well respected provider.
For what it's worth, when I'm hiring someone for a role with regulatory remit I don't generally expect them to know everything verbatim - that's a job for a lawyer or an extremely senior position for which considerable experience is expected
You're unlikely to walk into a job with sole responsibility for regulatory affairs, so at the start of the career path it's more about being able to demonstrate some knowledge in this area, genuine curiosity, and a reasonable idea about where to go to find relevant information and how to use it when you get it.
If you manage to read all of the list above and all the associated guidance, and memorise it all, then you'll be extremely unusual - but you will find that you get to a position where you know roughly which reg is the relevant one for some types of question that you may come across. The more you use it the more you'll remember, so you can e.g. look out for question at work or on here and see if you can decide how you'd go about answering them.