There are two types of flexible working - non-statutory and statutory, these are explained in broad terms here:
Non-statutory request: A non-statutory request for flexible working isn’t governed by law. If your employer has an internal procedure around flexible working, follow it. If they don’t, you may want to consider some of the ideas we provide later.
A non-statutory request might work for you if you’re not covered by flexible working legislation. You might also want to make a non-statutory request if you’re not sure if flexible working is for you, and you just want to try it out. Or if you want to work flexibly but only for a short time.
Statutory request: A statutory request for flexible working is governed by law. If you make this kind of request, you need to put your request in writing and your employer must discuss it with you before they make any decision.