BSc and further career in Academia on different subject Currently pursuing a Bachelor if Finance, but I have a huge interest on Statistics. I was wondering whether BSc in a non technical subject (With technical I mean Statistics, Mathematics, Computer Science etc.) affects a potential academic career in Statistics. 

Can MSc and PhD in Statistics or Applied Mathematics enable an academic career in these fields?
You might check in advance the application requirements for the MSc and/or PhD in Statistics or Applied Mathematics. By doing so, you will have a better overview on the technical competences you have to show to receive admission to the program.

In addition, you can show your interest by taking part or leading extracurricular activities with strong technical components (e.g., programming clubs, competitive programming, and so on.). Admission boards not only take into account your degree but the sum of your experience and potential.