As you know, investment banking is incredibly competitive. However, I would not let your weaker A level results deter you if this is what you want to do - particularly as you have a 2.1 and have a place at LSE to do your Masters. If you do well here, then the A level results become less relevant.
Don't beat yourself up about the poor A Level results - rather spend your energy thinking about how you can deal with this if it comes up and present it in a positive light - so for example, don't say you didn't do well - rephrased you could say I got X grades after only 9 months study and have since proved myself by gaining a 2.1 at Reading etc, etc.
Sometimes we build what we think of as a weakness up so that it predominates our thinking when it would be more helpful for us to acknowledge it and then move on to what we have achieved.
There is a good article on the five hurdles that applicants face in when applying to investment banking in the news items of this website - which may help. Also visit
www.efinancial.co.uk for more advice on applying to investment banks
Good Luck!