Quant Graduate

Hello! I am graduating next year and I would like some advice in launching a graduate role in trading or quant research. I have a spring week (UK version of 1st year internships for those who are not familiar) experience in a top quant firm, but I could not manage to get an internship in the field that I want this year, for some reason I failed in the AC stage three times. I believe that the reason is that I am a pure math major and everything else I learn is extra. Could you give me some recommendations on what sites or books would help me study?
I have read and imagine that it is extremely unlikely nowadays to get in without one into a FO role. If that was your situation too, what did you do next? Your advice would help me a lot, and maybe someone else who is in a similar situation as me.
I don't think your resume would be outright rejected for the lack of an internship, at least for graduate trader positions at trading companies and assuming you come from a good undergraduate program and have good marks. The bigger challenge is, as you have already experienced, making it through the process. Not having an internship will mean you lack some context compared to your competition though. Getting into a quant research role will be very hard with an undergraduate degree.