You will have a claim in the employment tribunal if your employer refuses to let you take annual leave. Your entitlement to holidays and holiday pay is determined by your employment contract, subject to the minimum provisions laid down in the Working Time Regulations 1998 (WTR 1998). Your employment contract can contain better provisions than WTR 1998. If they do, those conditions become a contractual right which you can enforce in the Employment Tribunal.
This Guide details your entitlement to holidays and holiday pay, and how to pursue a claim in the Employment Tribunal for your rights.