It is not unusual for holiday entitlements to be subject to the operational requirements of the organisation.
Such restrictions might only allow you to take annual leave at certain times of the year, for example at company shut down times. The organisation may also limit the number of days that may be taken at any one time.
You should consult your written statement of particulars (and/or your contract of employment), which should set out your annual leave entitlement and which may also identify any restrictions concerning when annual leave might be taken.
Under the Working Time Regulations, you have a legal right to at least 5.6 weeks paid leave in the year (equivalent to 28 days a year for those working 5 days a week), though an employer can count bank and public holidays towards this total. Speak to your manager to see whether you can negotiate a period to take your annual leave which suits both you and the organisation.
If annual leave periods are flexible, and your manager is refusing any dates you suggest, check whether the dates you suggest coincide with busy periods of work. Talk to work colleagues and find out when they have requested their annual leave for, how much notice they gave and whether your dates clash with theirs, or whether they have suffered similar responses from the manager.
If work colleagues have been granted their requests for leave, and your dates do not coincide with busy periods, then take the matter up with senior management. Speak to your union representative if you are a member of a union.
If these informal methods of enquiry fail you may have to pursue your case through your organisation's formal grievance procedure.
If, despite raising a formal grievance, your manager refuses you all or part of your leave entitlement (ie. you are prevented from taking your full 5.6 weeks quota), consider whether to bring a tribunal claim. Seek advice before going down this route, and remember that there is a 3-month time limit for bringing such claims.