Someone who works full-time and get's 20 days holiday will effectively be paid 20 days x 8 hours (for example).
On a part-time basis this would be 10 days x 8 hours (for example).
So in essence it is NOT about the number of days/time you have off, but the hours your employer has to pay for your holiday.
If you normally work two days a week, for example, you are entitled to 4 weeks off, covering those two days.
If you think that the average week is 5 days, then 20 days is 4 weeks, which is the legal minimum entitlement.
Therefore, you can have 4 times your normal working week as holidays, whatever that amounts to.
You don't say if you work complete days (but only some of them each week), or everyday (but a reduced number of hours per day). Either way you should work out your holiday entitlement in hours, not days. That makes it simpler to understand if you are being short-changed. You should receive (in hours) a direct % of the working week of a full-timers.
The others above have kind of intimated this.
The same applies to Public Holidays. There are 10 of these in the UK, and you should have (in hours) a proportionate number of hours applied for time off for PHs.
It depends how many hours you are working, as most holidays will be allocated on a pro rata basis.
If a full timer works 40 hours and gets 20 days holiday, a part timer who works 20 hours a week should get 10 days plus 50% of any public holidays.
If you work more hours, you holiday entitlement should be a pro rata percentage of the annual entitlement, i.e. somebody working 30 hours per week should get 15 days holiday plus three quarters of the public holidays.