An employees right to paid leave from work is wrapped up in the Working Time Regulations 1998, which grants all employees the equivalent of 5.6 weeks holiday per annum, for full time workers in the UK this normally equates to 28 days.
The issue of whether or not an employer has the right to refuse a holiday request does crop up, especially where the employee wishes to take the time off at a time which does not suit the business or where there are already lots of staff with time booked off for the same period.
Under the Working Time Regulations 1998 they allow an employer to refuse a holiday request as long as they give counter notice that is equal to or more than the time off that the employee has requested.
Example
An employee approaches you on the 1st June requesting 10 days off work starting 1st July.  In order to refuse this request an employer would need to write to the employee (via email or other) by the 20th June stating why the leave has not been granted.
This requirement only applies if there is no agreement (i.e the employee does not have a contract) between the employee and employer about how much notice an employee should give before taking paid leave from work.
Holiday Contract Clause
To avoid the need to do this, it is good practice to include in an employees contract a statement requiring them to give notice and seek managerial approval before any holiday is given.  If this clause exists an  employer may refuse a request without having to give formal counter notice as long as they respond swiftly to any request, i.e In January the employee requests 1 week off on the 1st June, the manager then refuses the request on 30th May, it would be seen that the employee has met their duty to inform their employer and any refusal could be unfair.
Enforcing time off
An employer does have the right to request that certain periods of the year are protected from holidays or require employees to set aside holiday days to cover periods of shut down at Christmas for example. Â Any such requirement should made clear to the employee in their contract of employment or in a separate holiday policy that the employee is made aware of.
Summary
Employers and managers do have the right to refuse holiday requests if they are incompatible with business needs, clash with other employees time off or where insufficient notice or authority is given.