Currently the Law states that parents of children under the age of six or disabled children under the age of eighteen have the right to apply for flexible working. This request must be in writing and can include different shift patterns, when you work, how long you work and where.
The employer is duty bound to consider your request and must be able to demonstrate why, if it is refused. You are entitled to take a colleague with you to any meetings regarding this issue. This may be your trade union representative if your company acknowledges unions.
If you feel that your employer has not reasonably demonstrated why they cannot accommodate your request, your company should have a policy on either flexible working or grievance. If you have a trade union representative, I suggest you seek advice from them. If not, the Human Resources department or another senior member of staff should advise you. Other useful agencies are ACAS and Citizens Advice Bureau.
See: ACAS (2007) Flexible working and work life balance. London. ACAS.