Hello Rachael. Yes, you are allowed to bring your family as a student. However, you need to be a full-time student. Additionally, your family can be your wife and children, but not other family members e.g. siblings.
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A dependant partner or child is one of the following:
1. your husband, wife or civil partner
2. your child should be under 18 years old
You’ll need to provide evidence of your relationship with them when you apply, for example: a marriage or civil partnership certificate for your partner, a birth certificate for your child.
Find out more here: Study abroad in the UK for international students