Currently, an employee (with 26 weeks of continuous employment) can request Flexible working if they have the responsibility of a child under 18 or are the carer of dependent adults. This year will see a relaxation of current legislation which will enable any employee (still requires 26 weeks continuous employment) to request flexible hours regardless of their reasoning or circumstance.
Obviously an Employer is well within their rights to reject any request that amends Working Hours from what was agreed in the Employment Contract. The Government have also relaxed the current formalities and timeframes in which an employer must respond to a request. In Theory this is to avoid a single mother receiving the same formal response to a request as John Smith who wants to take Scuba Diving more seriously. An Employer is enabled to take longer to assess, discuss, or work with individuals to reach a solution which works for everybody (Or tell John to find an evening class!).