Undergrad newbie with questions about internships

First, a bit about me (I apologise if this comes across as too vague or too much of an essay, this is my first ever post on this site):

19, M, Sophomore @ University of Nottingham (UK), Business with French and Spanish.

All A's and A*'s at GCSE and A level (Geography, History, English Lit., French), which I'm guessing is 4.0 GPA.

Previously interned at a law firm and a Media/PR company in London, spent this summer working for a medical communications company. Planning to set up an online business with a close friend this academic year.

Sadly I only recently adopted a real interest in finance and squandered a lot of opportunities in freshman year to network, join societies and committees, etc. related to finance or attaining "positions of leadership" which I understand banks look highly upon when looking at an applicant's experience and ECA's. My interest was aroused mainly by FX and stock paper trading which I took up this summer.

A few questions I have are:

- I never took Maths A level and my degree is non-mathematical/quantitative. Will this hold me back from securing an internship at a BB or Boutique? The areas I'm interested in arte corporate banking, investment banking and equity research

- To compensate for my relatively indifferent freshman year I am going to try like hell to compensate by participating in societies such as SIFE (Students in Free Enterprise), AIESEC (Association Internationale d'Etudiants en Sciences Economiques et Commerce), and of course the financial society. Is active membership in these considered to be highly regarded, or are you needed to be a part of the committee/in a role of responsibility in order for employers to be impressed?

- Is off-cycle internship competition as fierce as positions for sumer analysts? I have a year abroad as part of my degree and think this would be an opportunity to get some financial working experience.

- Given my situation (non-quantitative degree, no previous financial work experience, not an Oxbridge/LSE/Imperial undergrad), would I be better working my rear end off in my degree and in work fields outside of banking to get into a top MBA school and then try to enter at associate level?

Apologies if I appear condescending/ignorant at any point, as mentioned I am very new to this site and to finance in general and have yet to get a grasp of the lingo, culture etc.