Do I have to say yes to a request for part-time working? Employment Law for Employers
If the request for part-time working is a flexible working request, you can only rely on one of the eight statutory reasons for refusing. These include burden of additional cost on the company, difficulty arranging other staff and detrimental impact on quality of service.
When considering such a request you should always keep in mind indirect discrimination as most requests for part-time working are from women and your approach must be as consistent as possible.