visa sponsorship for investment banking internship

So many threads on this. In short, no.

You may qualify for the J1 visa, if your business contacts have that process going in their firm or you can go through an agency that sponsors the J1 for you.

Since you don't study in the US, you don't qualify for F1, or the subsequent OPT opportunities.

Thousands of coaches, interns, au pairs, and students use the J1 visa category every year and it's a path that should work out if the corporate side gets along with it. 

I don't know which visa you would need for the UK, sorry.

If the J1 route isn't working for you, there are other opportunities to briefly live in the US:

• exchange semester, either through your university or through your own research/contacts
• enroll in the US on F1 for a full academic year during or after your studies to qualify for OPT
• Work for a EU/UK company that has FLDP, rotation schemes, or training schemes abroad
• The H1b visa now also offers "self sponsorship", although  students or no work experience don't qualify. It would depend on our specific skill set and how much of a salesperson you could be. H1b is also a lottery, so YMMV. This might work if you already have extensive experience through jobs, there are some students who work full-time while studying also.