Financial firms don't want to hire school leavers for internships. That's really the long and short of it I think...I mean what are they going to have that person do? They are unlikely to trust them to do any substantive work so the internship would either be doing very basic admin work (which you could just as well find anywhere that isn't a "major firm") or fetching tea and coffee.
I think you need to manage your expectations here really. There might be some shadowing type opportunities but even those I imagine are few and far between, and likely only a couple days or a week at most I'd think. Plus, it's practically summer already so if there were any such things available they've probably been set in stone long since...
If you want to work over the summer before your degree, look at local jobs. If you want something that might be vaguely useful experience wise (even just for your own sake) then try and see what office type jobs you can find rather than customer service related roles. Sign up with a temp agency and see what they have.