Children's diets contain too few fruits and vegetables and too many foods high in saturated fat. Food intake is affected by multiple individual and family factors, which may differ for core foods (that are important to a healthy diet) and non-core foods (that are eaten more for pleasure than health). Data came from a sample of twins aged 11 years (n 342) and their parents from the Twins Early Development Study. Foods were categorised into two types: core (e.g. cereals, vegetables and dairy) and non-core (e.g. fats, crisps and biscuits). Parents' and children's intake was assessed by an FFQ. Mothers' and children's preference ratings and home availability were assessed for each food type. Parental feeding practices were assessed with the child feeding questionnaire and child television (TV) watching was maternally reported. Physical activity was measured using accelerometers. Correlates of the child's consumption of each food type were examined using a complex samples general linear model adjusted for potential confounders. Children's non-core food intake was associated with more TV watching, higher availability and greater maternal intake of non-core foods. Children's core food intake was associated with higher preferences for core foods and greater maternal intake of core foods. These results suggest that maternal intake influences both food types, while preferences affect intake of core foods but not of non-core foods, and availability and TV exposure were only important for non-core food intake. Cross-sectional studies cannot determine causality, but the present results suggest that different approaches may be needed to change the balance of core and non-core foods in children's diets.