Do you know what stockbroking actually is? Or is it merely a term perpetuated by the media and cinema, that you've tagged along to?
I'm going to get one thing out of the way before I go any further - walk into an interview in the City and tell the person in front of you that your personal portfolio makes you a prime candidate for the position in question, and you will be laughed out the door.
I'm not here to be condescending, I'll happily answer any questions you have, but you're making brash assumptions about things you don't seem to know too much about.
First, read:
http://www.amazon.co.uk/Need-Know-About-City-Guides/dp/0955218632Don't do a thing until you've read that cover to cover.
In reference to your initial post:
1 bank runs a gap-year internship scheme - Rothschild's is an advisory firm, thus they have no markets function within their business. Unless you have contacts at banks/brokerage houses, it's simply a no go.
Dropping Maths may well be the worst decision you ever made.
Banking, trading, broking, whatever: it's quantitative, analytical, logically based - Maths is intrinsic to all of the aforementioned.
Universities will see Economics and Business, taken as seperate A-Levels as conflicting given the amount of overlapping material - you may disagree, but it's their view, not mine.
Law is regarded as a "soft A-Level" by both Cambridge and the LSE - another point to consider.
I'm not trying to write-off your chances before you even try, I'm just trying to be realistic.
To the third point: Unless you are predicted & achieve an A/A* in Maths, you will struggle to gain a place at the universities which make up 95% of Front Office City intern/graduate intake. One of the most important things to consider is that what you do at university speaks volumes, to the extent where it may make your university irrelevant - however dedication and effort is key.
Going to somewhere such as Liverpool and applying for a FO markets position will result in nothing. In an equities Sales(broking)/Trading assessment centre in November, I was with LSE, Cambridge, Oxford, UCL (myself), SSE & Bristol students, who read either Economics or Maths.
It's competitive and harsh - if you're seeking to make "£££" in the City, you haven't been reading the news enough, this isn't 2004.