People come into investment banking from different backgrounds. Be sure to follow financial journals (Financial Times and the Economist) to demonstrate your interest. If you do a finance BSc, aim for a top university, as this may help in securing a banking internship or full time job. In contrast to BSc's, MBAs typically have a few years of experience. They usually come from diverse backgrounds including finance and engineering, and it is important to note that a good number of MBAs do the degree to switch careers; however I believe that you can definitely do an MBA from a non-business background.
I’m not an investment banker or anything like that but; if you start to learn some things about business, finance and brokering through the internet, news websites like the Economist and Trading apps like yahoo finance and Investmate. Then maybe you’ll have enough knowledge to be able to talk really well in your personal statement or interview about what you want to do? I’m sure you’ll be able to get into a university