I'm not a City lawyer but work in a profession/suity job where I've worked alongside one or two over the years. My advice:
-outright lechs are rare, but beware the male senior colleagues who will have you trailing along as an entourage because you are young and pretty and therefore enhance their status, who are dismissive of you in front of others and will never actually give you any responsibility or chance to prove yourself (they do that for the male trainees). In my experience that type of man is depressingly common in a lot of professions, though less as time goes by, thank goodness. It is difficult to handle-I've been that woman, many years ago. You can only make sure: (i) you never play up to this (no hair twirling, simpering, dressing a bit too sexy or flashy), keep things cool and professional, rise above the slights; (ii) you network madly with more useful people; and (iii) you volunteer to do work and make very sure there is good work product from you that people can judge you on;
-don't assume anything about your colleagues. it may look like a very white, male-dominated, privately-educated and Oxbridge environment but you can't necessarily tell by looking what people's education, class backgrounds or sexuality is, nor what race their partners are etc. I've known many a trainee really offend people with assumptions, whether because they are v right-on and cynically assume we are all bigoted Establishment shits, or very right-wing and conservative and assume the black bloke over there only got in by some kind of positive discrimination;
-FIGHT YOUR CORNER, albeit politely, where your work and ideas are concerned. It is very irritating when a trainee comes up with something potentially promising then can't argue for it or explain the idea. If you can't do this for your colleagues, they will assume you won't be able to do it for clients. Prepare, take a risk. It is better to be wrong (understandably, and due to inexperience) than never to try, and never, seemingly, to think about the task in hand;
-what my father told me, when I started work: don't be afraid to show liking for people you genuinely get on with. It is possible, especially for women, to be so concerned about demeanour that you end up as a bit of an automaton. But provided it is authentic, you don't need to hide the fact you like people;
-keep in touch with professional bodies and associations, find a mentor.
The last solicitor I worked with has a trainee whose appearance is a little startling (hair extensions, a LOT of make-up, very tight clothes, mega heels). I don't care about that myself, though other clients certainly will, but coupled with the fact she literally NEVER did anything useful, not even help lug the files, nor come up with a single useful piece of info like a date we couldn't find, appear to know any details of the problem or even fetch anyone a coffee, I will be very surprised to see her again in future meetings.
Take heart from nightmare trainee stories. There are plenty of numpties out there who will thin out the numbers nicely, leaving a smaller field for you to compete with.