Yes. You can turn down a specific holiday request, as long as you're not stopping someone taking their statutory minimum leave across the year. The usual approach is to give notice at least as long as the leave asked for, so two weeks' notice to refuse a two-week request, and to be consistent about it.
Refusing leave fairly comes down to genuine business reasons and being consistent, not picking and choosing. Blanket or one-rule-for-some refusals, especially where a protected reason might be in play, are where complaints tend to start.
Every situation has its own details, and those details change the right answer. For a read on yours, take the free Employee Situation Check or book a call.
General guidance to help you decide your next step, not legal advice. Employment law changes, so always check the current position for your own situation.
