Every worker, whether part-time or full-time, covered by the working time regulations 1998 is entitled to a minimum of 5.6 weeks paid annual leave. This is equivalent to 28 days for someone working five days a week, and calculated on a pro-rata basis for part-time employees.
For example, an employee who works three days a week is entitled to just under 17 days paid holiday (16.8 days exactly) - their normal working week multiplied by three. This is because one week of holiday time is the same amount of time that an employee would normally work in a week.
With regard to public holidays, these can be counted as part of the statutory 5.6 weeks holiday entitlement. There is no statutory right to take bank holidays off. Therefore, unless you include specific details in an employee's contract of employment which states there is a right to paid time off for bank holidays, you are not obliged to pay that staff member for those days, unless they take them as part of their annual leave entitlement.