Under the Flexible Working Regulations 2014, you can refuse for business reasons—like cost or customer impact—but must reply within 28 days (2024 update) and offer an appeal.
A clear, justified rejection letter helps, and exploring compromises can dodge discrimination claims. Legal input ensures your decision holds up if challenged. Meet with the employee to discuss their request—it shows good faith and might reveal a workable tweak. Keep a log of all requests to spot trends and refine your policy.
Helpful government guidance is available at: Flexible working on GOV.UK.