As long as you are an employee, and you have been working continuously for your employer for at least 26 weeks, you have the right to make a request to work flexibly, and for your employer to consider that request.
In the past, the right to make a request to work flexibly was limited to employees with caring responsibilities for children or vulnerable adults, but since 2014, any employee with 26 weeks’ service can make a request.
Your employer must not discriminate unlawfully against you, for example on grounds of gender, when deciding whether to agree to your request. Speak to your union rep if you are not sure, or to Citizens’ Advice if you are not a member of a union.
Your employer may offer better rights on flexible working, beyond the statutory minimum regime. You should check your contract of employment and other documents, such as your staff handbook, to find out your entitlement with your current employer.
Improving benefits and entitlements on flexible working has been a priority for unions, so if you work for an organisation that recognises unions you are very likely to have access to more generous flexible working rights.