Can banks legally charge late fees in addition to interest on overdue payments?

They can/cannot - depending on the market in which they operate and the regulator.

Banks publish something called a Schedule of Charges - these are the charges they can levy to their customers. Check with your bank and ask for this. All charges that banks charge you, have to be published.

A Schedule of Charges will let you know if they can charge a fee in addition to the interest for late payments (most do, citing it as administrative fees).