This thread has come up time and time again, and people attempt to answer it based on their opinions. I too was unsure about what uni course etc to choose, however I thought the best option would be to ask the banks itself what they believe is the best.
One of my friends did a programme at JP morgan and I asked him to ask the recruiting staff the questions on my behalf. They said that course choice didnt matter so much as what University you go to. To find out what Universities are considered 'good', the best thing is to find out which universities the banks do campus recruiting from. You can do this by going on the website and the universities come down in a drop down menu. The ones Ive seen from various banks are Oxford, Cambridge, Imperial,LSE, UCl, Warwick, Kings and Bristol. Considering he/she said that this is the best indication of the type of universities they want you to come from, it is perhaps best to try and go to one of these.
Quantitive degrees are not essential although they may give you an advantage.