Some people have contracts which state that they're only employed for specific periods of the year. (e.g. it's not unusual for school support staff, such as kitchen assistants, to have 'term time only' contracts). If so, they don't get paid outside of their employed periods (except that they'll still be entitled to a certain amount of paid holiday, calculated pro rata to a full year's employment).
However I'll assume that you've got a 'normal' contract, so that you're regarded as 'employed' throughout the whole year. If so, your statutory (paid) holiday entitlement is 5.6 times the number of days you work each week. (If you work a different number of hours each day the calculation will be be based upon hours instead of days. i.e. your holiday entitlement, measured in hours, will be 5.6 times times 21 hours = 117.6 hours).
Your employer is free to determine when your paid holidays should be (subject only to providing you with adequate notice of those dates). When a business is closed for any period (such as over Christmas), any days which an employee would normally work become 'enforced holidays'. i.e. the employee should be paid as normal but will lose those days from their remaining holiday entitlement.
Some employers provide more than the statutory minimum holiday allowance. If so, they are free (subject to any individual contractual arrangements) to make their own rules regarding holidays as long as they ensure that the employee's basic rights (referred to in the preceding paragraph) are maintained, and that part-timers aren't treated less (or more) favourably than full-timers.
Incidentally, public holidays have no special significance in employment law. If you normally worked on a Friday your employer could insist that you turned up for work on Christmas Day, at normal pay rates, and discipline you if you failed to do so.
Chris