What happens about bank holidays?

The annual entitlement is whatever is in the contract (subject to the min 5.6 weeks). Bank holidays are not an extra entitlement.

Holiday pay is when you pay an employee for time when they did not have to work (ignoring sickness or other reasons you might pay them).

So, if you pay them on a bank holiday and they did not work then it uses up a day of their annual entitlement.