As has been indicated, public holidays have no significance whatsoever in employment law. they're 'just another day'. If, for example, someone normally works on the day of the week upon which Christmas Day falls, their employer has every right to demand that they attend work on that day, at their normal rate of pay. If the employee failed to attend, they could be disciplined.
The only statutory right to paid holidays relates to the total number of days holiday per year. It's 5.6 times the number of days worked each week (capped at 28 days). So an employee working 5 days per week will have a statutory entitlement to 28 days paid holiday. The employer is free (subject to providing reasonable notice) to determine when those days are taken. It would be perfectly lawful for an employer to say that someone's holidays were the first Tuesday and the fourth Thursday in every month, with the second Wednesday in the first four months. The employee would never get 3 days in a row off, yet alone a week or a fortnight to go away, but the law would have been complied with.
All that designating the Royal Wedding Day as a public holiday has done, for some people, is to force them to be on holiday on that date (thus losing a day's holiday at another time of the year, when it would have been more convenient for them).
Chris