Are my parents entitled to benifits if I am under 18 and only work part time (no education)?

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I am being pestered by my parents to sign up with connextions, because I have left education and I am just working part time hours an apparently they are entitled to £20 a week for me not being full time work can someone tell me if this is true or give me a link or number or something? Thanks

Are my parents entitled to benifits if I am under 18 and only work part time (no education)?