Since you handle cash, I think you'll struggle with EMIs. The vast majority of them outright refuse to touch any business that's involved in cash. Regulators don't like it when e-money institutions handle physical money.
Most currency exchanges use traditional banks. But it's very hard (nearly impossible) to get an account nowadays unless you have very large volumes, excellent AML, and every check on the company comes back squeaky clean.
Lloyds, Barclays, NatWest, and several smaller banks work with companies similar to yours.