The conditions that apply to your spouse and children's stay in the UK will be shown on a stamp or sticker in their passport. The stamp or sticker will say how long they are allowed to stay in the UK for. It will usually be for the same amount of time as you. If it does not state that they must not work or enter employment, then they are free to work.
If the immigration official issuing it is satisfied that you, the student, have been given permission to stay in the UK for 12 months or more, your dependants should receive the stamp or sticker that allows them to work. If you are not staying for 12 months or more, they will receive the stamp or sticker that does not allow them to work.
Please see the UKCOSA website for further details. Student Advice and Welfare Services at UWE can provide more guidance.