Bank holidays have no official standing in employment legislation. It's only the total number of paid holidays per year that are defined by law.
The law states that the number of days you must be given in holiday must be a minimum of 5.6 x the number of days that you work in a week. (That doesn't apply to people who work 6 days per week though, since the total is capped at 28 days). So, for you, that's 16.8 paid days off each year.
In the first year of employment that figure has to be rounded up to 17 days. Thereafter the 0.8 of a day can either be dealt with by giving the employee a day off but only paying them 80% of their pay for that day or by giving them 16 days off plus 80% of a day's pay in addition to what they'd normally receive. (Many employers though will voluntarily round up the figure anyway, giving the employee 17 full-paid days off).
Remember that all 'enforced holidays' (e.g. when the business is closed, such as Christmas Day) are included within that total.