If part-timers work the same number of days, but shorter hours, they will be entitled to 28 days (5.6 working weeks equivalent) holiday – they will just be shorter days.
If they work less days, you have to calculate a pro-rata entitlement, which can be a bit complicated ……
Firstly, divide the full allowance including bank holidays (e.g. 28 days) by the number of days worked for a full time worker (e.g. 5).  Then multiply this by the number of days worked by the part-timer (e.g. 3).  So, in this example: 28 ÷ 5 x 3 = 16.8 days.  Next, work out how many bank holidays fall on the employee’s working days in that holiday year and deduct these from the total to show the number of holidays left for the employee to take.
If the part-timer works an irregular number of hours, such as 4 hours on a Monday and Thursday and 8 hours on a Wednesday, it is best to work out the holiday entitlement in hours.
First, calculate the number of hours worked by a full timer – e.g. 37.5 hours x 52 weeks = 1950.  Work out the full time holiday allowance in hours – e.g. 28 days x 7.5 hours = 210.  Then work out the hours worked by the part-timer – in this example 16 hours x 52 weeks = 832.  Divide the part-timer’s hours by the full-timer’s hours which is 832 ÷ 1950 = 0.43.  Multiply that sum (0.43) by the full-time holiday allowance in hours, which in this case is 0.43 x 210 = 90.3 hours.  Finally, you will need to deduct the bank holidays that fall on working days.  Then have a well earned rest and a nice cuppa!