As Ethel states, public holidays have no special status in employment law. If a public holiday falls on a day when you would normally work, the employer has every right to expect you to work as normal, at your normal pay rate and with no time off in lieu. (e.g. if Scrooge & Co decide that their office will be open on Christmas Day, they can insist that their staff attend for work at normal pay rates).
Some employees have special arrangements regarding public holidays written into their contracts but, unless such arrangements exist (or unless the employer decides to display his/her generosity on an ad hoc basis), you've no right to extra pay, or time off in lieu, for working on a public holiday.
Chris