common answer the question
from an old poly?
Yes of course you can - from Russell Group unis at least. I know of several people working in top law firms with English degrees from various top 20 law firms. I understand the same applies to other City jobs like banking.
If it's a top 20 uni, then yes you can, but you'll need that outside your degree you have a keen interest in finance; a good way to do this is set up a (small-scale) trading account. I've got a friend doing History at KCL who's been very successful mainly because of that.
Re Muncrun - Your degree matters more for banking than law; for banking there's a much greater bias towards economics/maths/physics etc, for top law firms anything (from a good uni) is fine.
Well, during some work experience i had the opportunity to go to Merril Lynch. Being very interested in investment banking myself, I was quite eager to find out the requirements of obtaining a job in the city. I found that it really doesn't matter what your degree is, as long as you have an aptitude for the job. The vice president of futures and options, for example, didn't even have a degree. Just three A-levels in Geography, History and English!