Lost Graduate trying to find his way into a Quant Shop

Hey guys, care to help a fresh graduate?

I've just finished an undergrad in Applied Physics with a 2:1 at a non target and i want to make a plan that will eventually land me a role as a quant. Since i don't have a stellar CV (no top 5 uni, no work experience, no math olympiad etc), and a masters degree not being an option, it seems very unlikely i'll get an entry level position at the moment. 

So i was thinking of getting a graduate role in Data Science, become very good a programming, learn the according math on the side and build projects to put on my cv that'll demonstrate my knowledge/skillset thats needed as a quant. After a year or two start applying for positions that are more on the data science side at quant shops and work my way up from there. Would there be a more direct approach such as getting an internship in something similar but not as competitive?

Honestly though, i'm quite lost at the moment and unsure how to proceed. So any sort of help regarding particular internships in quantitative finance, a different route etc would be greatly appreciated!