EU/EEA Nationals
If your spouse is an EEA national they will be able to work without restriction, unless they are a national of the Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Slovakia or Slovenia ('A8' Countries), then they may be required to register as a worker under the 'Worker Registration Scheme'. There is a one-off fee of £90 to register. Note that registration may take some time. For more information visit Working in the UK website.
If you or your dependents are from Romania or Bulgaria, they are allowed to work in the UK with similar restrictions that apply to non-EU/EEA dependants. They will need to apply for permission to work. You are recommended to speak to an advisor in the Student Advice and Welfare Services to discuss the restrictions. Alternatively, full information can be found on the Working in the UK website.
Non-EEA Nationals
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. If the immigration official issuing the stamp 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 that will not allow them to work.
For more information contact Student Advice and Welfare Services.