Unfortunately, under the Working Time Regulations 1998 (WTR), you do not have the right to determine when you take your annual leave. Therefore, if your employer has a genuine business reason, it does not have to agree to your dates.
The Regulations allow your employer to require you to give notice, equal to twice the length of the holiday requested. Your employer can also insist that you take your holiday at a particular time.
However, if you feel that your employer is refusing your request unreasonably, you might consider whether it is discriminating against you. If you can show that other people without your protected characteristics (e.g. race, gender, etc.) have been treated more favourably, you may be able to complain of a breach of the Equality Act 2010.
Your employer must, at some stage within the annual leave year, allow you time to use up your leave entitlement.