Also worth keeping in mind - do you really think you're going to get anything out of any opportunity at this point in life? They aren't going to allow a 16 year old to do anything other than make tea. Can you even imagine what would be the outcome if it came out they were allowing unpaid 16 year olds on work experience do literally anything in a financial institution related to the actual function of that institution?
The best case scenario would you be just sitting next to someone going through excel spreadsheets all day and being on calls (a lot of which you probably won't be allowed to listen to). This is not interesting for you nor does it really give a great deal of insight into the sector or role, I imagine. It also is completely useless when it comes to applying to your first job, which almost certainly isn't going to be a graduate role but some generic customer/food service type role - who want to see if you have any work experience at all that involved actually doing anything.
I think you're really missing the point of what your year 10 work experience is for.