www.citizensadvice.org.uk/work/rights-at-work/holidays-and-holiday-pay1/taking-your-paid-holiday/
Your employer can refuse your holiday request if they give you the correct notice. If they keep refusing and it’s stopping you taking your holiday, it’s worth talking to them to find out why. If you can’t you might have to make a claim to an employment tribunal.
If they keep refusing your request so that you’re not able to take your holiday in the current leave year, you can claim they’ve refused to allow you to take holiday. You would have to start early conciliation within 3 months less one day of the date on which you wanted your holiday to start.
landaulaw.co.uk/holidays/
How much notice do I need to give my employer before I take my holidays?
The general notice period for taking leave is at least twice as long as the amount of leave you want to take (unless there is a more informal arrangement with your employer or your contract of employment says otherwise). For example, you need to give 2 weeks notice for 1 week’s leave, or 2 days’ notice for 1 day’s leave- unless your contract says something different.
Can my employer refuse my request for holiday, even if I have already booked it?
Yes, your employer can refuse your holiday request, for example during busy periods. If you have already booked your time off, your employer must give as much notice for you to cancel it as the amount of leave you have requested. For example, your employer must give 2 weeks’ notice to refuse your booked holiday if the leave you requested was for 2 weeks.
Although your employer can refuse to give you holiday leave at a certain time, they cannot refuse to let you take your minimum leave entitlement of 28 days for the year.