The conditions that apply to your husband or wife's stay in the UK will be shown on a stamp or sticker in their passport. They should receive the stamp or sticker that allows them to work if the immigration official issuing it is satisfied that you, the student, has been given permission to stay in the UK for twelve months or more. If it does not say that they must not work or enter employment, then they are free to undertake either paid or voluntary work.
If this is not the case, and they have received the stamp or sticker that does not allow them to work, they will not be able to undertake any paid work but this does not necessarily mean that they cannot undertake any non-paid voluntary work. You are advised to arrange an appointment with a student adviser in Student Advice and Welfare Services (SAWS) to discuss the situation.