What is the legal age to move out of your parents house in the UK?

A child may move out at 16 if they have their legal guardian's permission.

If the child does not have permission to move out at 16, they can still do so, but the guardians can get a court order to make the child move back home (this rarely happens).

In terms of renting: A child (classed as a person under 18 years of age) cannot legally hold a tenancy agreement, therefore they would need to arrange a joint tenancy (where one of the holders is an adult) or a tenancy in trust where an adult (such as a friend or Social Services) will hold the tenancy on the child's behalf.