>>13025820I'd recommend double majoring in some combination of math, stats, or CS. Keep in mind, you pretty much need a degree in CS to go into most proprietary trading / HFT shops. But if even you don't pick CS as one, make sure you learn to program decently, particularly with python -- it's pretty much industry standard.
Also, try to get as many quant-related internships as you can. Getting names on your resumes is all that matters. For me, at least in the US, it was pretty much impossible to find any relevant internships coming from a non-target school. Having projects relating to any sort of modeling or ML are a decent substitute though. One of the hottest areas right now in banks is with Natural Language Processing.
It's possible to get full-time from undergrad with a good enough resume, but usually most roles at good firms require some sort graduate education. I ended up going for my masters in Fin Eng and that's how I got my foot in the door, but most STEM masters will be sufficient. Its also very common for people to come after PhD, but there's the cost/benefit of spending the time to do one.