As a carer for a disabled family member or acquaintance, you are covered by the Equality Act, which states that you must not be directly discriminated against due to your association with a disability. Examples of this type of discrimination are being refused a job or otherwise being treated less favourably at work due to your caring responsibilities. Your Force should have a policy for allowing carers to apply for adjusted shifts, flexi-time or part-time working.
For more information, the Carers UK website has an information page on your rights. There is also a PDF prepared by the Government Equalities Office on how the Equality Act affects you as a carer.