otnememUhm, we are in a scathing mood aren't we. Well, if humour won't do it for you let's try and be more helpfully pragmatic then.
Firstly, firms do care an awful lot about the reputation of your institution. Although their seemingly egalitarian admission policies openly state that they will look at the individual and not at the university he/she went to, that is partially true only for traditional red brick universities -- hence, Greenwich doesn't qualify unless, like I said before, you have excellent grades. Even amongst traditional universities there are considerable disparities. Large city firms have an approximate intake of 50% from Oxbridge -- so those geeks at Magdalene college have considerably higher chances of getting a TC than you do, oh omnipotent multi-tasking deity -- with a good chunk of the rest coming from either London's better institutions, i.e. UCL, LSE and King's -- most definitely not Greenwich regardless of how good their sports facilities are -- or the other relatively prestigious faculties of the likes of Nottingham, Durham and Bristol. Hence, if you are even remotely serious about a career in law, you wouldn't consider Kingston, Greenwich or the UEL, as the "only universities in London which would slightly interest you" (Essex being the only remote exception).
In any case, your dismissal of Oxford is quite irritating, if not offensive. You may have decent predictions but not nearly good enough to be even considered for a place - in a way, you are doing nothing but denigrating something you can't reach, not a very noble thing to do.
Also, if you can be bothered to get to Metropolitan University, whose very poor law faculty is located in the very central, and admittedly attractively positioned, Moorgate campus, I really don't see why you couldn't do the same for UCL (Euston -- three stops above Moorgate on the Northern Line) or King's and LSE (Covent Garden). Well, in any case, you probably don't have the requisite grades to go to any of these.
Thirdly, the firms mentioned in my post that you have never heard of are amongst the 6 largest in London (hence England, hence, for most of them anyway, the world). So, once again, if you are even remotely interested in a career in law, I suggest you start learning those names.
A considerably more reasonable option would have been to apply to those (relatively good) institutions that match your predicted grades. On the top of my head, something along the lines of City, yes still in central London, or hell even King's (you may have a chance after all) - thus still giving you a possibility, albeit reduced, to try for the bigger firms, provided you get good degree marks.
Anyway, it's your judgment, it's your life, one can merely advice. Maybe your business enterprise - that you are so keen on embarking upon at the same time as your law degree - will prove to be immensely successful, thus affording you the, somewhat improbable, possibility of giving the finger to all those "geeky" Oxford graduates, struggling to earn a meagre 50k as newly qualified associates in the city.