chances of getting into high finance?

Before you read this, i know nothing about finance so excuse my mistakes if i make any. 

im currently a student doing my a levels, (in final year of sixth). My subjects are history, politics and business studies. (hopefully A*AA) and i was thinking of applying to universities like durham, notts, kcl, qmu and maybe bath/bristol to do history.

I am not necessarily interested in finance, and i never exactly have been. My main goal was to convert into law after i've finished my history degree, and then most likely try and pass the bar. However, after some second thought certain aspects of finance are beginning to appeal to me. Firstly, because of the extremely fast paced environment, the importance of the work you are completing and opportunities within the industry itself if you decide to exit.

Secondly, and primarily according to some of the people i spoke to while i was doing my school work experience at Visa's legal department, getting into banking (and i am assuming m&a) isn't too much of a career change if you're a solicitor at a mc firm in London when considering that they virtually do very similar things in regards to working on contracts and negotiations etc etc.

so this got me thinking that breaking into finance isn't entirely out of the picture, but what i really wanted to ask was if its possible to gradually break into high finance after getting a few years of exp somewhere else, and what i mean by that is do i have a good chance to apply and get into a position at a more mediocre bank/firm (from doing history at one of the unis ive previously mentioned), build my way up and then try and get an offer for a bank like Credit Suisse or a firm like state street. Im not just aiming for IB, because i know that's probably out of the picture. Im looking into more general and probably less prestigious tenets of finance like asset management, PE/CV (maybe? not sure) but hopefully you get the point.

Id be willing to eat my words if i need to, so dont be afraid to tear me apart if im delusional or wrong. I know id probably have to get a masters and go to some business school and maybe get this certification and that. I solely just want to know if its possible.

just to add, I have relative in finance who worked at Credit Suisse and then started his own fund with a few colleagues, so if i do end up following this path, i might be able to get a good reference and what not.